Transcript Holt CA Course 1

1-8 Solving Equations by Subtracting
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
1-8 Solving Equations by Subtracting
Warm Up
Determine whether each value is a solution.
1. 86 + x = 102 for x = 16
yes
2. 18 + x = 26 for x = 4
no
3. x + 46 = 214 for x = 168 yes
4. 9 + x = 35 for x = 26
Holt CA Course 1
yes
1-8 Solving Equations by Subtracting
California
Standards
AF1.1 Write and solve one-step
linear equations in one variable.
Holt CA Course 1
1-8 Solving Equations by Subtracting
Vocabulary
inverse operations
Holt CA Course 1
1-8 Solving Equations by Subtracting
h + 14
82
h
?
h + 14
h
Holt CA Course 1
82
68
The equation h + 14 = 82 can be
represented as a balanced scale.
To find the value of h, you need h
by itself on one side of a balanced
scale.
To get h by itself, first take away
14 from the left side of the scale.
Now the scale is unbalanced.
To rebalance the scale, take away
14 from the other side.
1-8 Solving Equations by Subtracting
Taking away 14 from both sides of the scale is
the same as subtracting 14 from both sides of
the equation.
h + 14 = 82
–14 –14
h = 68
Subtracting a number is the inverse, or
opposite, of adding that number. Inverse
operations are operations that undo each
other. If an equation contains addition, solve it
by subtracting from both sides to “undo” the
addition.
Holt CA Course 1
1-8 Solving Equations by Subtracting
Additional Example 1A: Solving Equations by
Subtracting
Solve the equation. Check your answer.
x + 87 = 152
x + 87 = 152
– 87 – 87
87 is added to x.
Subtract 87 from both
sides to undo the addition.
x = 65
Check x + 87 = 152
?
Substitute 65 for x in the
equation.
65 + 87 = 152
?
152 = 152  65 is the solution.
Holt CA Course 1
1-8 Solving Equations by Subtracting
Additional Example 1B: Solving Equations by
Subtracting
Solve the equation. Check your answer.
72 = 18 + y
72 = 18 + y
–18 –18
54 =
y
Check 72 = 18 + y
?
72 = 18 + 54
?
72 = 72 
Holt CA Course 1
18 is added to y.
Subtract 18 from both
sides to undo the addition.
Substitute 54 for y in the
equation.
54 is the solution.
1-8 Solving Equations by Subtracting
Additional Example 2: Social Studies Application
Johnstown, Cooperstown, and Springfield are located
in that order in a straight line along a highway. It is
12 miles from Johnstown to Cooperstown and 95 miles
from Johnstown to Springfield. Find the distance d
between Cooperstown and Springfield.
distance between
Johnstown and
Springfield
95
=
=
95 = 12 + d
–12
–12
83 =
d
distance between
Johnstown and
Cooperstown
12
+
+
distance between
Cooperstown and
Springfield
d
12 is added to d.
Subtract 12 from both sides to undo
the addition.
It is 83 miles from Cooperstown to Springfield.
Holt CA Course 1
1-8 Solving Equations by Subtracting
Check It Out! Example 1A
Solve the equation. Check your answer.
u + 43 = 78
u + 43 = 78
– 43 – 43
u
43 is added to u.
Subtract 43 from both
sides to undo the addition.
= 35
Check u + 43 = 78
?
35 + 43 = 78
?
78 = 78 
Holt CA Course 1
Substitute 35 for u in the
equation.
35 is the solution.
1-8 Solving Equations by Subtracting
Check It Out! Example 2
Patterson, Jacobsville, and East Valley are located in
that order in a straight line along a highway. It is 17
miles from Patterson to Jacobsville and 35 miles from
Patterson to East Valley. Find the distance d between
Jacobsville and East Valley.
distance between
Patterson and East
Valley
35
=
=
35 = 17 + d
–17 –17
18 =
d
distance between
Patterson and
Jacobsville
17
+
+
distance between
Jacobsville and East
Valley
d
17 is added to d.
Subtract 17 from both sides to
undo the addition.
It is 18 miles from Jacobsville to East Valley.
Holt CA Course 1
1-8 Solving Equations by Subtracting
Check It Out! You try this one…
Solve the equation. Check your answer.
68 = 24 + g
68 = 24 + g
–24
–24
44 =
g
Check 68 = 24 + g
?
68 = 24 + 44
?
68 = 68 
Holt CA Course 1
24 is added to g.
Subtract 24 from both
sides to undo the addition.
Substitute 44 for g in the
equation.
44 is the solution.
1-8 Solving Equations by Subtracting
Lesson Quiz
Solve each equation.
1. x + 15 = 72
x = 57
2. 81 = x + 24
x = 57
3. x + 22 = 67
x = 45
4. 93 = x + 14
x = 79
5. Kaitlin is 2 inches taller than Reba. Reba is
54 inches tall. How tall is Kaitlin? 56 inches
Holt CA Course 1