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Solving Two-Step
Equations
You will solve equations by undoing operations
using properties of equality.
Essential Question: How do you solve two-step
equations?
EXAMPLE 1
Solve a two-step equation
Solve x + 5 = 11.
2
x + 5 = 11
2
x + 5 – 5 = 11 – 5
2
x =6
2
2 x =2 6
2
x = 12
Write original equation.
Subtraction Property of Equality
Simplify.
Multiplication Property of Equality.
Simplify.
ANSWER
The solution is 12. Check by substituting 12 for x in
the original equation.
EXAMPLE 1
CHECK
Solve a two-step equation
x + 5 = 11
2
12 + 5 ?= 11
2
11 = 11
Write original equation.
Substitute 12 for x.
Simplify. Solution checks.
GUIDED PRACTICE
for Example 1
Solve the equation. Check your solution.
1. 5x + 9 = 24
SOLUTION
5x + 9 = 24
5x + 9 – 9 = 24 – 9
5x = 15
5x 15
=
5 5
x=3
Write original equation.
Subtraction Property of Equality
Simplify.
Division Property of
Equality
Simplify.
GUIDED PRACTICE
for Example 1
ANSWER
The solution is 3. Check by substituting 3 for x in the
original equation.
CHECK
5x + 9 = 24
?
5 3 + 9 = 24
24 = 24
Write original equation.
Substitute 3 for x.
Simplify. Solution check.
GUIDED PRACTICE
for Example 1
Solve the equation. Check your solution.
2. 4y – 4 = 16
SOLUTION
4y – 4 = 16
4y – 4 + 4 = 16 + 4
4y = 20
4y 20
=
4
4
y=5
Write original equation.
Addition Property of Equality
Simplify.
Division Property of Equality.
Simplify.
GUIDED PRACTICE
for Example 1
ANSWER
The solution is 5. Check by substituting 5 for y in the
original equation.
CHECK
4y – 4 = 16
?
4(5) – 4 = 16
16 = 16
Write original equation.
Substitute 5 for y.
Simplify. Solution checks.
GUIDED PRACTICE
for Example 1
Solve the equation. Check your solution.
z
3. – 1 = 3 –7
SOLUTION
–1= z –7
3
–1+7= z –7+7
3
z
6=
3
z
3 6=3
3
18 = z
Write original equation.
Add 7 to each side.
Simplify.
Multiply each side by 3.
Simplify.
GUIDED PRACTICE
for Example 1
ANSWER
The solution is 18. Check by substituting 18 for z in
the original equation.
CHECK
–1= z –7
3
? 18
–1=
–7
3
–1= –1
Write original equation.
Substitute 18 for z.
Simplify. Solution checks.
EXAMPLE 2
Solve a two-step equation by combining like terms
Solve 7x – 4x = 21
7x – 4x = 21
3x = 21
3x = 21
3
3
x=7
Write original equation.
Combine like terms.
Divide each side by 3.
Simplify.
GUIDED PRACTICE
for Examples 2 and 3
Solve the equation. Check your solution.
5.
8t – 3t = 35
8t – 3t = 35
5t = 35
5t = 35
5
5
t =7
Write original equation.
Substract the like terms
Divide each side by 5
Simplify.
GUIDED PRACTICE
CHECK 8t – 3t = 35
8(7) – 3(7) =? 35
?
56 – 21 = 35
35 =35
for Examples 2 and 3
Write original equation.
Substitute 7 for t.
Multiply.
Simplify. Solution checks.
GUIDED PRACTICE
for Example 4
Jobs
10. Kim has a job where she makes $8 per hour plus
tips. Yesterday, Kim made $53 dollars, $13 of which was
from tips. How many hours did she work?
SOLUTION
53 = 13 + 8h
53–13 = 13 –13 + 8h
40 = 8h
5=h
Write the equation
Subtraction Property of Equality.
Simplify.
Division Property of Equality
GUIDED PRACTICE
for Example 4
ANSWER
She worked for 5 hours

How do you solve two-step
equations?
Essential Question: