example 1
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EXAMPLE 1 Solving an Equation Using Subtraction
ANSWER
The solution is –23.
– 8 – 8Original equation
Subtract 8 from each side to undo addition.
Simplify. x is by itself.
= –15 + 8x
= –15 + 8x
x –23=
EXAMPLE 2 Solving an Equation Using Addition
c – 4.5 = 13
c – 4.5 + 4.5 = 13 + 4.5
c = 17.5
Original equation
Add 4.5 to each side to undo subtraction.
Simplify. c is by itself.
Check Substitute 17.5 for c
in original equation.13 = 13 ✓
c – 4.5 = 13
=? 1317.5 – 4.5
EXAMPLE 3 Using a Model
Rock Climbing
SOLUTION
Use the diagram to help you write an algebraic model. Let x represent the distance left to climb.
A cliff has a height of about 1500 feet. If you have already climbed 675 feet, how much farther do you have to climb to reach the top?
EXAMPLE 3 Using a Model
1500 = x + 675
1500 – 675 = x + 675 – 675
825 = x
Write an algebraic model.
Subtract 675 from each side.
Simplify. x is by itself.
ANSWER
You have about 825 feet left to climb.
GUIDED PRACTICE for Examples 1, 2, and 3
Solve the equation. Check your solution.
1. x + 9 = 20
x + 9 = 20
c + 9 – 9 = 20 – 9
x = 11
Original equation
Subtract 9 from each side.
Simplify. x is by itself.
Check Substitute 11 for x
in original equation.11 = 11 ✓
=? 1311 + 9
GUIDED PRACTICE for Examples 1, 2, and 3
2. –10 = 3 + y
–10 = 3 + y
–10 – 3 = 3 + y – 3
–13 = y
Original equation
Subtract 3 from each side.
Simplify. y is by itself.
Check Substitute –13 for y
in original equation.–10 = –10 ✓
3 – 13 =?
–10
GUIDED PRACTICE for Examples 1, 2, and 3
3. m – 14 = –15
m – 14 = –15
m – 14 + 14 = –15 +14
m = –1
Original equation
Add 14 from each side.
Simplify. m is by itself.
Check Substitute –1 for m
in original equation.–1 = – 1 ✓
=? –15–1 – 14
GUIDED PRACTICE for Examples 1, 2, and 3
2 = z – 6.4
2 + 6.4 = z – 6.4 + 6.4
8.4 = z
Original equation
Subtract 6.4 from each side.
Simplify. z is by itself.
Check Substitute 8.4 for z
in original equation.2 = 2 ✓
4. 2 = z – 6.4
=? 8.4 – 6.4 2
GUIDED PRACTICE for Examples 1, 2, and 3
s + 49 = 162
s + 49 – 49 = 162 – 49
s = 113
Write an algebraic model.
Subtract 49 from each side.
Simplify. s is by itself.
SOLUTION
Let s represent Jerry’s seashells
5. Seashells
Lucinda combines her 49 seashells with Jerry’s seashells, for a total of 162. Write and solve an addition equation to find how many seashells Jerry had before their collections were combined.
ANSWERJerry had 113 seashells before their collections were combined
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