Transcript Chapter 2 - Crestwood Local Schools

Properties of Numbers
PRE-ALGEBRA LESSON 2-1
At the Red Valley Sports Camp, 15 kids went horseback riding, 14
played tennis, 23 went hiking, and the rest of the campers stayed in
their cabins. If 83 kids were in the camp, how many stayed indoors?
31
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
(For help, go to Lesson 1-5.)
Simplify.
1. –18 + (–7)
2. 32 – (–3)
3. (–13) + 6
4. 2 – 48
Check Skills You’ll Need
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
Solutions
1. –18 + (–7) = –25
2. 32 – (–3) = 32 + 3
= 35
32 – (–3) = 35
3. (–13) + 6 = –7
4. 2 – 48 = 2 + (–48)
= –46
2 – 48 = –46
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
Carlos spent $42 on his golf game. He then bought
a bottle of water for $2 and a chef’s salad for $8. What was
the total cost for his golf game and meal?
You can use the Associative Property of Addition to find the total
cost in two different ways.
42 + (2 + 8) = 42 + 10 = 52 Add 2 and 8 first.
(42 + 2) + 8 = 44 + 8 = 52 Add 42 and 2 first.
Carlos’s total cost was $52.
Quick Check
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
Name each property shown.
a. 17 + x + 3 = 17 + 3 + x
Commutative Property of Addition
b. (36  2)10 = 36(2  10)
Associative Property of Multiplication
c. km = km • 1
Identity Property of Multiplication
d. (103 + 26) + 4 = 103 + (26 + 4)
Associative Property of Addition
Quick Check
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
Use mental math to simplify (48 + 7) + 2.
(48 + 7) + 2
= (7 + 48) + 2 Use the Commutative Property of Addition.
= 7 + (48 + 2) Use the Associative Property of Addition.
= 7 + 50
Add within parentheses.
= 57
Add.
Quick Check
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
Suppose you buy school supplies costing $.45,
$.65, and $1.55. Use mental math to find the cost of these
supplies.
0.45 + 0.65 + 1.55
= 0.65 + 0.45 + 1.55
Use the Commutative Property of Addition.
= 0.65 + (0.45 + 1.55)
Use the Associative Property of Addition.
= 0.65 + 2.00
Add within parentheses.
= 2.65
Add.
The cost of the school supplies is $2.65.
Quick Check
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
Use mental math to simplify (20 • 13) • 5.
(20 • 13) • 5 = (13 • 20) • 5
Use the Commutative Property of
Multiplication.
= 13 • (20 • 5)
Use the Associative Property of
Multiplication.
= 13 • 100
Multiply within parentheses.
= 1,300
Multiply.
Quick Check
2-1
Properties of Numbers
PRE-ALGEBRA LESSON 2-1
Name each property shown.
1. d  1 = d
Identity Property of Multiplication
2. 3 + (2 + 5) = (3 + 2) + 5
Associative Property of Addition
3. f  g = g  f
Commutative Property of Multiplication
4. 32 + 45 + 102 = 45 + 32 + 102
Commutative Property of Addition
2-1
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Evaluate each expression.
a. 24 – 6 ÷ 2 • 4 + 36
48
b. 6 • (3 – 1) + 18
30
2-2
c. 10 + 6 • 5 – 4 ÷ 2
38
The Distributive Property
PRE-ALGEBRA LESSON 2-2
(For help, go to Lesson 1-2.)
Simplify each expression.
1. 3 • 7 – 9
2. (9 – 5)6
3. 8 + 2 • 6
4. 2(6 – 3)
5. 4 • 5 – 4 • 3
6. 3 • 2 – 1 • 2
Check Skills You’ll Need
2-2
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Solutions
1. 3 • 7 – 9
2. (9 – 5) • 6
21 – 9
4•6
12
24
3. 8 + 2 • 6
4. 2 • (6 – 3)
8 + 12
2•3
20
6
5. 4 • 5 – 4 • 3
6. 3 • 2 – 1 • 2
20 – 12
6
8
–
4
2-2
2
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Use the Distributive Property to find 15(110) mentally.
15(110) = 15(100 + 10)
Write 110 as (100 + 10).
= 15 • 100 + 15 • 10
Use the Distributive Property.
= 1,500 + 150
Multiply.
= 1,650
Add.
Quick Check
2-2
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Ms. Thomas gave 5 pencils to each of her 37
students. What is the total number of pencils she gave to
the students?
(37)5 = (40 – 3)5
Write 37 as (40 – 3).
= 40 • 5 – 3 • 5
Use the Distributive Property.
= 200 – 15
Multiply.
= 185
Subtract.
Ms. Thomas gave the students 185 pencils.
Quick Check
2-2
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Simplify 11(23) + 11(7).
11(23) + 11(7) = 11(23 + 7)
Use the Distributive Property.
= 11(30)
Add within parentheses.
= 330
Multiply.
Quick Check
2-2
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Use algebra tiles to multiply 4(3x – 4).
Model four
groups of
3x – 4.
Group like tiles.
So 4(3x – 4) = 12x – 16.
Quick Check
2-2
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Multiply.
a. –9(2 – 8y)
–9(2 – 8y) = –9(2) – (–9)(8y)
Use the Distributive Property.
= –18 – (–72y)
Multiply.
= –18 + 72y
Simplify.
b. (5m + 6)11
(5m + 6)11 = (5m)11 + (6)11 Use the Distributive Property.
= 55m + 66
Multiply.
Quick Check
2-2
The Distributive Property
PRE-ALGEBRA LESSON 2-2
Use the Distributive Property to simplify.
1. 15(203)
2. 7(180)
3,045
1,260
3. 6(26) – 6(16)
4. (8a – 4)9
72a – 36
60
5. 2(14 + y)
28 + 2y
2-2
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
Use numbers to write the following word expression: eight and
one-third minus five and two-sevenths.
8 1 –5 2
3
7
2-3
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
(For help, go to Lesson 2-2.)
Simplify each expression.
1. 5(b + 4)
2. –3(2x + 5)
3. 4(–8 – 3q)
4. –6(2b – 7)
Check Skills You’ll Need
2-3
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
Solutions
2. –3(2x + 5) = –3(2x) + (–3)(5)
1. 5(b + 4) = 5(b) + 5(4)
= –6x – 15
= 5b + 20
3. 4(–8 – 3q) = 4(–8) + 4(–3q)
4. –6(2b – 7) = –6(2b) + (–6)(–7)
= –32 – 12q
= –12b + 42
2-3
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
Name the coefficients, the like terms, and the
constants in 7x + y – 2x – 7.
Coefficients: 7, 1, –2
Like terms: 7x, –2x
Constant: –7
Quick Check
2-3
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
Simplify 9 + 4f + 3 + 2f.
9
+
4f
+ 3 + 2f
6f
+
12
Quick Check
2-3
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
Simplify 2b + b – 4.
2b + b – 4 = 2b + 1b – 4
Use the Identity Property of
Multiplication.
= (2 + 1)b – 4
Use the Distributive Property.
= 3b – 4
Simplify.
Quick Check
2-3
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
Simplify (7 – 3x)5 + 20x.
(7 – 3x)5 + 20x = 35 – 15x + 20x
Use the Distributive Property.
= 35 + (–15x + 20x)
Use the Associative
Property of Addition.
= 35 + (–15 + 20)x
Use the Distributive Property
to combine like terms.
= 35 + 5x
Simplify.
Quick Check
2-3
Simplifying Variable Expressions
PRE-ALGEBRA LESSON 2-3
Name coefficients, like terms, and constants.
1. 4f – 2f + 3
2. z + 2y – 14
4, –2; 4f, –2f; 3
1, 2; none; –14
Simplify each expression.
3. 3(a + c – 1) – 2c
4. 4(4v) – 4(v – 9)
3a + c – 3
12v + 36
2-3
Variables and Equations
PRE-ALGEBRA LESSON 2-4
Evaluate 10 – c for c = 10.
5
8
2-4
Variables and Equations
PRE-ALGEBRA LESSON 2-4
(For help, go to Lesson 1-1.)
Write a variable expression for each phrase.
1. the sum of x and 46
2. four less than g
3. t decreased by five
4. the quotient of z and 26
Check Skills You’ll Need
2-4
Variables and Equations
PRE-ALGEBRA LESSON 2-4
Solutions
1. the sum of x and 46
x plus 46
x + 46
2. four less than g
g minus 4
g–4
3. t decreased by five
t minus 5
t–5
4. the quotient of z and 26
z divided by 26
z
26
2-4
Variables and Equations
PRE-ALGEBRA LESSON 2-4
State whether each equation is true, false, or an
open sentence. Explain.
a. 3(b – 8) = 12
open sentence, because there is a variable
b. 7 – (–6) = 1
false, because 13 =/ 1
c. –9 + 5 = – 4
true, because – 4 = – 4
Quick Check
2-4
Variables and Equations
PRE-ALGEBRA LESSON 2-4
Write an equation for Six times a number added to the
number is the opposite of forty-two. State whether the equation is
true, false, or an open sentence. Explain.
Words
Equation
six times the number
added to
the
number
6x
added to
x
is
–42
6x
+
x
=
–42
is
the opposite
of forty-two
The equation is an open sentence, because there is a variable.
Quick Check
2-4
Variables and Equations
PRE-ALGEBRA LESSON 2-4
Is 45 a solution of the equation 120 + x = 75?
120 + x = 75
120 + 450
75
Substitute 45 for x.
165 =/ 75
No, 45 is not a solution of the equation.
Quick Check
2-4
Variables and Equations
PRE-ALGEBRA LESSON 2-4
A gift pack must hold 20 lb of food. Apples weigh 9 lb and
cheese weighs 5 lb. Can the jar of jam that completes the package
weigh 7 lb?
Words
weight of
apples
Let
Equation
j
plus
weight of
weight of
plus
cheese
jam
is
20 lb
=
20
= weight of jam.
9
+
5
+
j
9 + 5 + j = 20
14 + j = 20
Add.
14 + 7
Substitute 7 for the variable.
20
21 =/ 20
No, the jar of jam cannot weigh 7 lb.
2-4
Quick Check
Variables and Equations
PRE-ALGEBRA LESSON 2-4
1. Is b + 3b = 15 true, false, or an open sentence?
open sentence
2. Write an equation for A number added to seven times the number is the
opposite of thirty-two. Is the equation true, false, or an open sentence?
7x + x = –32; open sentence
3. Is 25 a solution of the equation 175 – x = 150?
yes
4. Can you stack eight books that are each 3 in. thick inside a box that is
18 in. tall?
no
2-4
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Lauralee pitched 12 innings. Maureen pitched 3 2 fewer innings.
3
How many innings did Maureen pitch?
8 1
3
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
(For help, go to Lesson 2-1.)
Simplify each expression.
1. 3 + 4 – 4
2. 7 + 9 – 7
3. 8 – 2 + 2
4. 6 + 2 – 2
Check Skills You’ll Need
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solutions
1. 3 + 4 – 4
= 3 + (4 – 4)
=3+0
=3
2. 7 + 9 – 7
= 9 + (7 – 7)
=9+0
=9
3. 8 – 2 + 2
= 8 + (2 – 2)
=8+0
=8
4. 6 + 2 – 2
= 6 + (2 – 2)
=6+0
=6
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solve y + 5 = 13.
Method 1
Method 2
y + 5 = 13
y + 5 – 5 = 13 – 5
y=8
Subtract 5
y + 5 = 13
from each side.
Simplify.
–5=–5
y=
8
Check y + 5 = 13
8 + 5 13
Replace y with 8.
13 = 13
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Larissa wants to increase the number of books in her
collection to 327 books. She has 250 books now. Find the number
of books she needs to buy.
Words
target number
Let
Equation
x
327
is
250
plus
number to buy
= number to buy.
=
250
2-5
+
x
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
(continued)
327 = 250 + x
327 = x + 250
327 – 250 = x + 250 – 250
77 = x
Use the Commutative Property of Addition.
Subtract 250 from each side.
Simplify.
Larissa needs to buy 77 more books.
Check Is the answer reasonable?
250 plus the number of books bought should
be a total collection of 327.
250 + 77 = 327
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solve c – 23 = – 40.
c – 23 = – 40
c – 23 + 23 = – 40 + 23
c = –17
Add 23 to each side.
Simplify.
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Marcy’s CD player cost $115 less than her DVD player. Her
CD player cost $78. How much did her DVD player cost?
Words
cost of CD player
Let
t
Equation
was
$115
less than
cost of DVD player
= cost of the DVD player.
78
=
t
–
115
78 = t – 115
78 + 115 = t – 115 + 115
193 = t
Add 115 to each side.
Simplify.
Marcy’s DVD player cost $193.
Quick Check
2-5
Solving Equations by Adding or Subtracting
PRE-ALGEBRA LESSON 2-5
Solve each equation.
2. 7 + f – 21 = –20
1. y + 8 = 12
–6
4
3. 67 = g – (–36)
31
4. Ricky rides his bike 12 miles every day. He stops after 7 miles to rest.
How much farther does he have to ride?
5 mi
2-5
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
Divide. Round each quotient to the nearest hundredth.
a. 0.5952
1.6
0.372, which rounds to 0.37
b. 10.5126
2.1
5.006, which rounds to 5.01
2-6
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
(For help, go to Lesson 1-9.)
Simplify each quotient.
1.
18
18
3. 21
–21
2.
–7
7
4. –13
–13
Check Skills You’ll Need
2-6
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
Solutions
1. 18 = 1
18
3.
21
= –1
–21
2. –7 = –1
7
4.
2-6
–13
=1
–13
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
288 pens are boxed by the dozen. How many boxes
are needed?
Words
number of pens
Let
Equation
b
288
is
12
times
number of boxes
•
b
= number of boxes.
=
12
2-6
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
(continued)
288 = 12b
288
12b
=
12
12
24 = b
Divide each side by 12.
Simplify.
24 boxes are needed.
Check Is the answer reasonable?
Twelve times the number of boxes is the number of pens.
Since 12  24 = 288, the answer is reasonable.
Quick Check
2-6
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
Solve –2v = –24.
–2v = –24
–2v
–24
=
–2
–2
v = 12
Check
Divide each side by –2.
Simplify.
–2v = –24
–2 • (12) –24
–24 = –24
Replace v with 12.
Quick Check
2-6
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
Solve x = – 5.
8
x
8 =–5
8 x = 8(–5) Multiply each side by 8.
8
x = – 40
Simplify.
Quick Check
2-6
Solving Equations by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-6
Solve each equation.
1. 8x = –48
2. –2x = 18
–6
–9
3. 108 = 9x
4.
v
= 14
–3
–42
12
n
5. –6 = 4
–24
2-6
Problem Solving Strategy: Guess, Check, Revise
PRE-ALGEBRA LESSON 2-7
Find three different odd numbers whose sum is 21. List all possibilities.
1, 3, 17; 1, 5, 15; 1, 7, 13; 1, 9, 11; 3, 5, 13; 3, 7, 11; 5, 7, 9
2-7
Problem Solving Strategy: Guess, Check, Revise
PRE-ALGEBRA LESSON 2-7
(For help, go to Lesson 1-5.)
Simplify.
1. 158 + 20
2. 158 + 30
3. 158 + 25
4. 158 + 22
5. In Exercises 1–4, which result came closest to 181?
Check Skills You’ll Need
2-7
Problem Solving Strategy: Guess, Check, Revise
PRE-ALGEBRA LESSON 2-7
Solutions
1. 158 + 20 = 178
2. 158 + 30 = 188
3. 158 + 25 = 183
4. 158 + 22 = 180
5. |181 – 178| = |3| = 3
|181 – 183| = |–2| = 2
|181 – 188| = |–7| = 7
|181 – 180| = |1| = 1
The result of Exercise 4, 180, is the closest to 181.
2-7
Problem Solving Strategy: Guess, Check, Revise
PRE-ALGEBRA LESSON 2-7
During the intermission of the play, the Theater Club sold cups
of popcorn and soda. The club sold 79 cups of popcorn and 96 sodas for
a total of $271. What was the selling price of a cup of popcorn? Of a
soda?
You can organize conjectures in a table.
As a first conjecture, try both with a price of $1.
2-7
Problem Solving Strategy: Guess, Check, Revise
PRE-ALGEBRA LESSON 2-7
(continued)
Popcorn Soda
Price
Price Total Price
$1
$1
79(1) + 96(1) = 79 + 96
= 175
The total is too low. Increase
the price of the popcorn only.
$2
$1
79(2) + 96(1) = 158 + 96
= 254
The total is too low.
Increase the price of the soda.
$2
$2
79(2) + 96(2) = 158 + 192 The total is too high.
= 350
Decrease the price of the popcorn.
$1
$2
79(1) + 96(2) = 79 + 192
= 271
The total is correct.
The popcorn price was $1, and the soda price was $2.
2-7
Quick Check
Problem Solving Strategy: Guess, Check, Revise
PRE-ALGEBRA LESSON 2-7
Solve using any strategy.
1. A sporting goods store manager ordered twice as many pairs of
basketball shoes as tennis shoes. He ordered 96 pairs in all. How
many pairs of each did he order?
32 pairs of tennis shoes; 64 pairs of basketball shoes
2. Manuel wrote a 512-word paper over the weekend. He wrote 180
more words on Sunday than he did on Saturday. How many words did
he write on Saturday?
166
2-7
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
Order from least to greatest: 1 , 0.25, 1 , – 0.5, 0.3,– 2
2
6
–2, – 0.5, 1 , 0.25, 0.3, 1
6
2
2-8
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
(For help, go to Lesson 1-4.)
Graph each set of numbers on a number line. Order the numbers from least
to greatest.
1. –3, 7, –9
2. –2, –10, –8
3. 0, 3, –5
4. 3, –6, 10
Check Skills You’ll Need
2-8
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
Solutions
1.
–9, –3, 7
2.
–10, –8, –2
3.
–5, 0, 3
4.
–6, 3, 10
2-8
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
Graph the solutions of each inequality on a
number line.
a. x > –2
An open dot shows that –2 is not a solution.
Shade all the points to the right of –2.
b. w >
– –5
A closed dot shows that –5 is a solution.
Shade all the points to the right of –5.
2-8
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
(continued)
c. k <
–4
A closed dot shows that 4 is a solution.
Shade all the points to the left of 4.
d. y < 6
An open dot shows that 6 is not a solution.
Shade all the points to the left of 6.
2-8
Quick Check
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
Write the inequality shown in each graph.
a.
x >
– –3
b.
x<3
Quick Check
2-8
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
Food can be labeled very low sodium only if
it meets the requirement established by the federal government.
Use the table to write an inequality for this requirement.
Label
Definition
Sodium-free food
Less than 5 mg per serving
Very low sodium food
At most 35 mg per serving
Low-sodium food
At most 140 mg per serving
2-8
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
(continued)
Words
a serving of very
low sodium food
Let
Equation
v
=
v
has at most
35 mg sodium
number of milligrams of sodium in a serving of
very low sodium food.
<
–
35
Quick Check
2-8
Inequalities and Their Graphs
PRE-ALGEBRA LESSON 2-8
1. Graph –7 >
– w.
2. Write an inequality for the graph.
x > –30
3. A child must be at least 50 in. tall to ride on the roller coaster. Write an
inequality for this situation.
h>
– 50
2-8
Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solve each equation.
a. n + 4 = 3
n = –1
b. 4 – p = 8
p=–4
2-9
Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
(For help, go to Lesson 2-5.)
Solve each equation.
1. m + 7 = 5
2. k – 8 = 11
3. 12 + h = 21
4. 6 = n – 23
Check Skills You’ll Need
2-9
Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solutions
1.
m+7=5
m+7–7=5–7
m=–2
2.
k – 8 = 11
k – 8 + 8 = 11 + 8
k = 19
3.
12 + h = 21
12 – 12 + h = 21 – 12
h=9
4.
6 = n – 23
6 + 23 = n – 23 + 23
29 = n
2-9
Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solve each inequality. Graph the solutions.
a. 4 + s < 12
4 + s < 12
4 + s – 4 < 12 – 4
s<8
b.
Subtract 4 from each side.
Simplify.
–16 >
– y – 14
–16 >
– y – 14
–16 + 14 >
– y – 14 + 14
–2 >
– y or y <
– –2
Add 14 to each side.
Simplify.
Quick Check
2-9
Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
You have 6 GB on your computer. The files you have
stored on the hard drive occupy at least 2 GB. How much storage
space is left for other files?
storage space
for our files plus
Words
Let
s
Inequality
2
storage
space left
is less than
or equal to
total
space
<
–
6
= storage space available.
+
s
2+s<
–6
2–2+s<
–6–2
Subtract 2 from each side.
s<
Simplify.
– 4
No more than 4 GB are left.
Quick Check
2-9
Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solve –10 < –13 + q.
–10 < –13 + q
–10 + 13 < –13 + 13 + q
3<q
Add 13 to each side.
Simplify.
Quick Check
2-9
Solving One-Step Inequalities by Adding or Subtracting
PRE-ALGEBRA LESSON 2-9
Solve each inequality.
2. –22 >
– g–6
–16 >
– g
1. e + 4 <
– 14
e<
– 10
3. A number q plus the opposite of 5 is less than or equal to 0.
q <
–5
2-9
Solving One-Step Inequalities by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-10
Solve each equation.
a. q ÷ 3 = 6
b. 7r = 21
q = 18
r=3
2-10
Solving One-Step Inequalities by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-10
(For help, go to Lesson 2-6.)
Solve each equation.
1. 6x = 24
x
3. –2 = 10
2. 63 = –7v
t
4. 6 = 48
Check Skills You’ll Need
2-10
Solving One-Step Inequalities by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-10
Solutions
1.
6x = 24
63 = –7v
2.
63
–7v
=
–7
–7
6x
24
=
6
6
–9 = v
x=4
3.
x
= 10
–2
x
–2
= –2(10)
–2
t
= 48
6
4.
6
x = –20
t
= 48(6)
6
t = 288
2-10
Solving One-Step Inequalities by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-10
A 1-ton truck has the ability to haul 1 ton, or 2,000 lb.
At most, how many television sets can the truck carry if each
TV set weighs 225 lb?
Words
is less than
number of
times 225 lb
2,000 lb
or equal to
televisions
Let x = number of televisions.
Inequality
x
•
225
225x <
– 2,000
2-10
<
–
2,000
Solving One-Step Inequalities by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-10
(continued)
225x < 2,000
225 – 225
x<
– 8.8
Divide each side by 225.
Simplify. Round the answer down to find a whole
number of television sets.
At most, the truck can carry 8 television sets.
Check Is the answer reasonable? The total weight of 8 television sets is
8(225) = 1,800 lb, which is less than 2,000 lb but so close that
another television set could not be carried. The answer
is reasonable.
Quick Check
2-10
Solving One-Step Inequalities by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-10
Solve z <
–2.
–8 –
z
< –2
–8 –
z
–8 –8 >
– –8(–2)
z>
– 16
Multiply each side by –8 and reverse
the inequality symbol.
Simplify.
Quick Check
2-10
Solving One-Step Inequalities by Multiplying or Dividing
PRE-ALGEBRA LESSON 2-10
Solve each inequality.
1. 3x >
– –27
x >
– –9
2. –5w > 15
1
3. 1 y <
–
4
2
4. –x <
0
5 –
y <
–2
x >
–0
w < –3
5. 4f > –12
f > –3
2-10