Transcript 1-11 - My CCSD

and
Subtraction
Equations
1-11
Addition
and
Subtraction
Equations
1-11Addition
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
1-11 Addition and Subtraction Equations
Warm Up
Determine if the given numbers are
solutions to the given equations.
1. x = 2 for 4x = 9
no
2. x = 5 for 8x + 2 = 42
yes
3. x = 4 for 3(x – 2) = 10
no
Course 2
1-11 Addition and Subtraction Equations
Problem of the Day
Four couples have dinner together. The wives are
Ginny, Helen, Sarah, and Bridget. The husbands are
Mark, Alex, Stephen, and Henry. Who is married to
whom?
• Sarah is Mark’s sister.
•
Sarah introduced Henry to his wife.
Bridget has 2 brothers, but her husband
is an only child.
•
Ginny is married to Stephen.
•
Ginny and Stephen, Helen and Mark, Sarah and
Alex, Bridget and Henry
Course 2
1-11 Addition and Subtraction Equations
Learn to solve one-step equations by
using addition or subtraction.
Course 2
1-11 Addition and Subtraction Equations
Vocabulary
Addition Property of Equality
inverse operations
Subtraction Property of Equality
Course 2
1-11 Addition and Subtraction Equations
To solve an equation means to find a solution to
the equation. To do this, isolate the variable—
that is, get the variable alone on one side of the
equal sign.
x=8–5
7–3=y
The variables are isolated.
x+5=8
7=3+y
The variables are not isolated.
Recall that an equation is like a balanced scale.
If you increase or decrease the weights by the
same amount on both sides, the scale will
remain balanced.
Course 2
1-11 Addition and Subtraction Equations
ADDITION PROPERTY OF EQUALITY
Words
You can add the
same amount to
both sides of an
equation, and the
statement will
still be true.
Course 2
Numbers
Algebra
2+3= 5
+4 +4
x = y
+z =+z
2+7= 9
x + z = y+ z
1-11 Addition and Subtraction Equations
Use inverse operations when isolating a
variable. Addition and subtraction are
inverse operations, which means that
they “undo” each other.
Course 2
1-11 Addition and Subtraction Equations
Additional Example 1: Solving an Equation by
Addition
Solve the equation b – 7 = 24. Check your
answer.
b – 7 = 24
+ 7 +7
b
= 31
Think: 7 is subtracted from b, so
add 7 to both sides to isolate b.
Check
b – 7 = 24
?
31 – 7 = 24
?
24 = 24
Course 2
Substitute 31 for b.
31 is a solution.
1-11 Addition and Subtraction Equations
Check It Out: Example 1
Solve the equation y – 3 = 21. Check your
answer.
y – 3 = 21
+ 3 +3
y
= 24
Think: 3 is subtracted from y, so
add 3 to both sides to isolate y.
Check
y – 3 = 21
?
Substitute 24 for y.
?
24 is a solution.
24 – 3 = 21
21 = 21
Course 2
1-11 Addition and Subtraction Equations
SUBTRACTION PROPERTY OF EQUALITY
Words
You can subtract
the same amount
from both sides of
an equation, and
the statement will
still be true.
Course 2
Numbers
Algebra
4 + 7 = 11
–3 – 3
x = y
–z = –z
4+4= 8
x–z=y–z
1-11 Addition and Subtraction Equations
Additional Example 2: Solving an Equation by
Subtraction
Solve the equation t + 14 = 29. Check your
answer.
t + 14 = 29
– 14 – 14
t
= 15
Think: 14 is added to t, so
subtract 14 from both sides to
isolate t.
Check
t + 14 = 29
?
15 + 14 = 29
?
29 = 29 
Course 2
Substitute 15 for t.
15 is a solution.
1-11 Addition and Subtraction Equations
Check It Out: Example 2
Solve the equation x + 11 = 36. Check your
answer.
x + 11 = 36
– 11 – 11
x
= 25
Think: 11 is added to x, so
subtract 11 from both sides to
isolate x.
Check
x + 11 = 36
?
25 + 11 = 36
?
36 = 36 
Course 2
Substitute 25 for x.
25 is a solution.
1-11 Addition and Subtraction Equations
Additional Example 3: Sports Application
The Giants scored 13 points in a game against
Dallas. They scored 7 points for a touchdown
and the rest of their points for field goals. How
many points did they score on field goals?
Let f represent the field goal points.
7 points
7
+
+
field goal points
f
=
=
points scored
13
7 + f = 13
–7
– 7 Subtract 7 from both sides to isolate f.
f= 6
They scored 6 points on field goals.
Course 2
1-11 Addition and Subtraction Equations
Check It Out: Example 3
A basketball player scored 23 points during a
game. Of those points, 3 were from 3-point goals
and the remainder were 2 point goals. How many
points did he score with 2 point goals?
Let x equal the points scored by 2 point goals.
3 point goals
+
2 point goals =
points scored
3
+
x
=
23
3 + x = 23
Subtract 3 from both sides to
–3
–3
isolate x.
x = 20
He scored 20 points from 2 point goals.
Course 2
1-11 Addition and Subtraction Equations
Lesson Quiz
Solve each equation. Check your answer.
1. x – 9 = 4
x = 13; 13 – 9 = 4
2.
3.
4.
5.
y = 66; 66 + 6 = 72
n = 62; 21 = 62 – 41
y + 6 = 72
21 = n – 41
127 = w + 31
81 = x – 102
w = 96; 127 = 96 + 31
x = 183; 81 = 183 – 102
6. Tamika has sold 16 dozen cookies this week.
This was 7 dozen more than she sold last
week. Write and solve an equation to find how
many dozen cookies she sold last week.
x + 7 = 16; 9 dozen
Course 2
and Subtraction
Equations
1-11
Multiplication
and Division
Equations
1-12Addition
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
1-11 Addition and Subtraction Equations
Warm Up
Solve.
1. x + 5 = 9
x=4
2. x – 34 = 72
x = 106
3. 124 = x – 39
x = 163
Course 2
1-11 Addition and Subtraction Equations
Problem of the Day
What 4-digit number am I?
• I am greater than 4,000 and less than
5,000.
• The sum of my hundreds digit and my ones
digit is 9.
• Twice my tens number is 2 more than my
thousands digit.
• The product of my hundreds digit and my
ones digit is 0.
• I am not an even number.
4,039
Course 2
1-11 Addition and Subtraction Equations
Learn to solve one-step equations by
using multiplication or division.
Course 2
1-11 Addition and Subtraction Equations
Vocabulary
Multiplication Property of Equality
Division Property of Equality
Course 2
1-11 Addition and Subtraction Equations
Like addition and subtraction, multiplication
and division are inverse operations. They
“undo” each other.
•
÷
Course 2
1-11 Addition and Subtraction Equations
If a variable is divided by a number, you can often
use multiplication to isolate the variable. Multiply
both sides of the equation by the number.
Course 2
1-11 Addition and Subtraction Equations
Additional Example 1: Solving an Equation by
Multiplication
Solve the equation h = 13. Check your answer.
2
h
2 = 13
(2) h
2 = 13(2)
h = 26
Check
Think: h is divided by 2, so
multiply both sides by 2 to
isolate h.
h
2 = 13
26 ?
= 13
2
?
13 = 13 
Course 2
Substitute 26 for h.
26 is a solution.
1-11 Addition and Subtraction Equations
Check It Out: Example 1
x
Solve the equation 5 = 30. Check your answer.
x
= 30
5
Think: x is divided by 5, so
(5) x
5 = 30(5)
x = 150
Check
multiply both sides by 5 to
isolate x.
x
5 = 30
150 ?
= 30
5
?
30 = 30 
Course 2
Substitute 150 for x.
150 is a solution.
1-11 Addition and Subtraction Equations
Remember!
You cannot divide by 0.
Course 2
1-11 Addition and Subtraction Equations
If a variable is multiplied by a number,
you can often use division to isolate the
variable. Divide both sides of the
equation by the number.
Course 2
1-11 Addition and Subtraction Equations
Additional Example 2: Solving an Equation by
Division
Solve the equation 51 = 17x. Check your
answer.
Think: x is multiplied by 17,
51 = 17x
so divide both sides by 17 to
51 = 17x
isolate x.
17
17
3=x
Check
51 = 17x
?
51 = 17(3)
?
51 = 51
Course 2
Substitute 3 for x.
3 is a solution.
1-11 Addition and Subtraction Equations
Check It Out: Example 2
Solve the equation 76 = 19y. Check your
answer.
Think: y is multiplied by 19,
76 = 19y
so divide both sides by 19 to
76 = 19y
isolate y.
19
19
4=y
Check
76 = 19y
?
76 = 19(4)
?
76 = 76
Course 2
Substitute 4 for y.
4 is a solution.
1-11 Addition and Subtraction Equations
Additional Example 3: Health Application
Trevor’s heart rate is 78 beats per minute.
How many times does his heart beat in 10
seconds?
Use the given information to write an equation,
where b is the number of heart beats in 10
seconds.
If you count your heart beats for 10 seconds and
then multiply that by 6, you can find your heart rate
in beats per minute.
Course 2
1-11 Addition and Subtraction Equations
Additional Example 3 Continued
Beats in 10s
b
times 6
· 6
6b = 78
6b = 78
6
6
b = 13
= beats per minutes
=
78
Think: b is multiplied
by 6, so divide both
sides by 6 to isolate b.
Trevor’s heart beats 13 times 10 seconds.
Course 2
1-11 Addition and Subtraction Equations
Check It Out: Example 3
During a stock car race, one driver is able to
complete 68 laps in 1 hour. How many laps
would he finish in 15 minutes?
Use the given information to write an equation,
where n is the number of laps completed in 15
minutes.
If you count the number of laps in 15 minutes and
multiply by 4, you can find the number of laps
completed in 1 hour.
Course 2
1-11 Addition and Subtraction Equations
Check It Out: Example 3 Continued
Laps in 15 min
n
times 4
·
4n = 68
4n = 68
4
4
n = 17
4
=
=
Laps in 1 hour
68
Think: L is multiplied
by 4, so divide both
sides by 4 to isolate n.
The driver would complete 17 laps in 15 minutes.
Course 2
1-11 Addition and Subtraction Equations
Lesson Quiz: Part I
Solve the equation. Check your answer.
1. 12 = 4x
x = 3; 12 = 4  3
2. 18z = 90
z = 5; 18  5 = 90
3. 12 = x
4
x = 48; 12 = x
4
4. 840 = 12y y = 70; 840 = 12  70
5. h = 9
22
Course 2
h = 198; 198 = 9
22
1-11 Addition and Subtraction Equations
Lesson Quiz: Part II
6. The cost of each ticket at the carnival was $0.25.
Li bought $7.50 worth of tickets. How many
tickets did she buy?
30
Course 2