Transcript Algebra II

Algebra II
1.3 Solving Equations
 In math, what are variables?
Letters that represent numbers.
 In math, what is an equation?
A mathematical expression to include an
equal sign.
Open sentence – a mathematical sentence
containing one or more variables.
 Write an algebraic expression to represent each
verbal expression.
 1A) 7 less than a number.

x–7
 B) three times the square of a number.

3x²
 C) the cube of a number increased by 4 times the
same number.

x³ + 4x
 D) twice the sum of a number and 5.

2 (x + 5)
 2A) 10 = 12 – 2

Ten is equal to twelve minus two.
 B) n + (-8) = -9

The sum of a number and -8 is -9.
 C) n/6 = n²

A number divided by six is equal to that

number squared.
Properties of Equality
Property
Symbols
Examples
Reflexive
A=A
-7 + n = -7 + n
Symmetric
If a= b, then b = a If 3 = 5x – 6,
then 5x – 6 = 3
Transitive
If a = b, and b = c, If 2x+1 = 7 and
then a = c
7 = 5x -8, then
2x+1 = 5x-8
Substitution
If a = b, then a
can replace b
If (4+5)m = 18,
then 9m = 18
 Name the property illustrated.
 3. 3m = 5n, and 5n = 10p, then 3m = 10p

Transitive property
 4. If -11a + 2 = -3a, then -3a= -11a + 2

Symmetric property
Warmup 8/31/12
 1. Write an example of the symmetric
property.
 2. Write an expression for 2(2x -6).
Problems
 Solve these equations.
 1. X + 14 = -7
-14 -14
X = -21
 2. 7 + 3x = 49
-7
-7
3x = 42
x = 14
 3. 1.8a – 5 = -2.3
+5 +5
1.8a = 2.7
a = 1.5
 4. -4(k + 7) = -12
-4k - 28 = -12
+28 +28
-4k = 16
k = -4
5. 7x + x – 3x = -24
5x = -24
x = -4.8
 6. 3d + 7 = 6d + 5
-6d
-6d
-3d + 7 = 5
-7 -7
-3d = -2
d = 2/3
Inequalities
 Rules for Multiplication / Division
– When you multiply / divide both sides by a
negative, you must __________ the sign.
 Try these and Graph on a number line:
 1. a + 2.5 < 3.7
 2. 5 ≥ 3x
Solving for a variable
 Place a box around the number you are
solving for. Move everything to the other
side using equation rules.
 Example1: Solve for r when d = rt
 Example 2: Solve for h when V = ⅓iir²h
Inequalities
 Rules for Multiplication / Division
– When you multiply / divide both sides by a negative, you must flip
the sign.
Try these and graph on a number line:
 1. a + 2.5 < 3.7
- 2.5 -2.5
a < 1.2
 2. 5 ≥ 3x
3x ≤ 5
x ≤ 5/3
Solve and Graph
3. 14 – 8n ≤ 0
-14
-14
-8n ≤ -14
n ≥ 7/4
4. 2 (4t + 9) < 18
8t + 18 < 18
-18 -18
8t < 0
t<0

Warmup 9/4/12
 1. Solve 4(x + 2) = 12
 2. Solve and graph: 2x + 6 < 12
Word Problems
7. Austin and Anna go to the West Bladen Bowling
alley. They have a total of $31 to spend on their
bowling adventure. It costs $3.50 to rent shoes
and $6.00 per game to bowl. Find the maximum
number of games that they can bowl if they each
rent shoes.
 What information should the variable represent?
The amount per game.
 Write the equation for the word problem and solve.
31 = 6.00x + 7.00
x = 4 games
8. Suppose Brandon and Barbie also go to
West Bladen Bowling alley but they have a
total of $60 to spend on bowling. Find the
maximum number of games that they can
bowl if they rent shoes. Let n be the
variable this time.
 Write an equation for this word problem and
solve.
60 = 6.00x + 7.00
x = 8 games
9. Larry spent $10,734
on his living expenses
last year. Most of
these expenses are
listed to the right. If he
paid rent 12 times last
year, how much was
Larry’s rent each
month?
Expense
Electric
Annual
Cost
$622
Gas
$428
Water
$240
Renter’s
Insurance
$144
Assignment
 In your workbook:
 Do page 3 (13-26 all)
 Do page 5 (1-16 all)
 ***Remember to show ALL work!!!