Download Solving Two-Step Equations

Solving Two-Step
Equations
You will solve equations by undoing operations
using properties of equality.
Essential Question: How do you solve two-step
equations?
TP: Construct and solve two step equations
for real world problems by combining like
terms
Steps for Solving Two-Step Equations
for any Addition or Subtraction on the
variable side of equation by “undoing” the
operation from both sides of the equation.
1.Solve
any Multiplication or Division from
variable side of equation by “undoing” the
operation from both sides of the equation.
Inverse Operations
Addition  Subtraction
Multiplication Division
2.Solve
Whatever you do to one side, you must do to
the other side to keep property of equality.
Example 1: Solve 4x – 5 = 15
4x – 5 =
+5
4x
=
4
x=5
Check:
15
+5
(Add 5 to both sides)
20
(Simplify)
4(Divide both sides by 4)
(Simplify)
4(5) -5 =15
20 – 5 = 15
15 =15
EXAMPLE 2
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 2
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 &2
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 3
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 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 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: