Solving TwoStep Equations

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Solving Two-Step Equations
10-1
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
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Learn to solve two-step equations.
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Sometimes more than one inverse operation is
needed to solve an equation. Before solving, ask
yourself, What is being done to the variable,
and in what order? Then work backward to undo
the operations.
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Additional Example 1 Problem Solving Application
The mechanics bill to repair Mr. Wongs car was
650. The mechanic charges 45 an hour for labor,
and the parts that were used cost 443. How many
hours did the mechanic work on the car?
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Additional Example 1 Continued
List the important information
The answer is the number of hours the mechanic
worked on the car.

• The parts cost 443.
• The labor cost 45 per hour.
• The total bill was 650.

Let h represent the hours the mechanic worked.
Total bill Parts Labor
650 443 45h
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Additional Example 1 Continued
Think First the variable is multiplied by 45,
and then 443 is added to the result. Work
backward to solve the equation. Undo the
operations in reverse order First subtract 443
from both sides of the equation, and then divide
both sides of the new equation by 45.
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Additional Example 1 Continued
650 443 45h
443 443 Subtract to undo the addition.
207 45h
Divide to undo multiplication.
4.6 h
The mechanic worked for 4.6 hours on Mr. Wongs
car.
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Additional Example 1 Continued
If the mechanic worked 4.6 hours, the labor would
be 45(4.6) 207. The sum of the parts and the
labor would be 443 207 650.
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Try This Example 1
The mechanics bill to repair your car was 850.
The mechanic charges 35 an hour for labor, and
the parts that were used cost 275. How many
hours did the mechanic work on your car?
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Try This Example 1 Continued
List the important information
The answer is the number of hours the mechanic
worked on your car.

• The parts cost 275.
• The labor cost 35 per hour.
• The total bill was 850.

Let h represent the hours the mechanic worked.
Total bill Parts Labor
850 275 35h
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Try This Example 1 Continued
Think First the variable is multiplied by 35,
and then 275 is added to the result. Work
backward to solve the equation. Undo the
operations in reverse order First subtract 275
from both sides of the equation, and then divide
both sides of the new equation by 35.
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Try This Example 1 Continued
850 275 35h
275 275 Subtract to undo the addition.
575 35h
Divide to undo multiplication.
16.4 ? h
The mechanic worked for about 16.4 hours on your
car.
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Try This Example 1 Continued
If the mechanic worked 16.4 hours, the labor
would be 35(16.4) 574. The sum of the parts
and the labor would be 275 574 849.
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Additional Example 2A Solving Two-Step Equations
Solve.
A. 7 22
Think First the variable is divided by 3, and
then 7 is added. To isolate the variable,
subtract 7, and then multiply by 3.
7 7 Subtract to undo
addition.
n 45
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Additional Example 2A Continued
Check
Substitute 45 into the original equation.
?
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Additional Example 2B Solving Two-Step Equations
B. 2.7 1.3m 6.6
Think First the variable is multiplied by 1.3,
and then 6.6 is added. To isolate the variable,
subtract 6.6, and then divide by 1.3.
2.7 1.3m 6.6
6.6 6.6
Subtract to undo addition.
3.9 1.3m
Divide to undo multiplication.
3 m
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Additional Example 2C Solving Two-Step Equations
Think First 4 is subtracted from the variable,
and then the result is divided by 3. To isolate
the variable, multiply by 3, and then add 4.
y 4 27
4 4 Add to undo subtraction.
y 31
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Try This Example 2A
Solve.
A. 5 29
Think First the variable is divided by 4, and
then 5 is added. To isolate the variable,
subtract 5, and then multiply by 4.
5 5 Subtract to undo
addition.
n 96
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Try This Example 2A Continued
Check
Substitute 96 into the original equation.
?
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Try This Example 2B
B. 4.8 2.3m 0.2
Think First the variable is multiplied by 2.3,
and then 0.2 is added. To isolate the variable,
subtract 0.2, and then divide by 2.3.
4.8 2.3m 0.2
0.2 0.2
Subtract to undo addition.
4.6 2.3m
Divide to undo multiplication.
2 m
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Try This Example 2C
Think First 2 is subtracted from the variable,
and then the result is divided by 4. To isolate
the variable, multiply by 4, and then add 2.
y 2 32
2 2 Add to undo subtraction.
y 34
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Lesson Quiz
Solve. 1. 3 10 2. 7y 25 24 3. 8.3
3.5x 13.4 4. 3 5. The cost for a
new cell phone plan is 39 per month plus a
one-time start-up fee of 78. If you are charged
1014, how many months will the contract last?
x 117
y 7
x 6.2
y 28
24 months