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Pre-Algebra
Two-Step Extension Homework
Mr. Masterjoseph
Name: _____________________
Class: _____________________
2016
Solve the following equations using the T- Chart Method. Check each answer by
substitution. The problems in bold pose a challenge. Try them!
Solve
Check
1. 2m + 9 = 39
2.
8t - 4 = 12
3.
b+2=6
6
4.
2m - 14 = 10
5.
8 + h = 10
4
6. 12b - 2b + 5 = 35
7. A cell phone plan costs $14.75 per month, plus $0.18 cents per minute. Lisa has
budgeted $35 a month for her cell phone. The equation $14.75 + 0.18m = $35
represents how many minutes Lisa can use each month. List the series of steps you
would take to solve the equation. Then give the solution
Solve
Check
8. At work, Jack must stuff 1000 envelopes with advertisements. He can stuff
12 envelopes in one minute, and he has 112 envelopes already finished.
Solve 1000 = 12n + 112 to find how many minutes it will take Jack to
complete the task.
Solve
Check
9. Create your own two – step equation word problem. You must use two of the
four operations (Addition, Subtraction, Multiplication, and Division).
Demonstrate the solution to your problem by showing all your work.
Solve Two-Step Equations A two-step equation contains two operations. To solve twostep equations, use inverse operations to undo each operation in reverse order. First, undo
addition/subtraction. Then, undo multiplication/division.
Sample 1
𝐜
Solve 𝟐 - 13 = 7
c
- 13 = 7
2
c
2
Write the equation.
- 13 + 13 = 7 + 13
c
2
2·
c
2
Addition Property of Equality
= 20
Simplify.
= 2 · 20
Multiplication Property of Equality
c = 40
Check:
c
2
40
2
- 13 = 7
- 13 = 7
20 - 13 = 7
7=7√
Sample 2
Solve 5y + 4 = 24
5y + 4 = 24
-4 = -4
5y = 20
5y = 20
5
5
y=4
Check: 5y + 4 = 24
5(4) + 4 = 24
20 + 4 = 24
24 = 24
Write the equation.
Subtraction Property of Equality.
Simplify.
Division Property of Equality
Simplify. Check your solution.
Sample 3
Solve 6y - 2y + 5 = 17
6y - 2y + 5 = 17 Write the equation.
4y + 5 = 17 Combine like terms.
4y + 5 = 17
-5 = -5 Subtraction Property of Equality.
4y = 12
Simplify.
4y = 12
4
4
Division Property of Equality.
y=3
Simplify. Check your solution.
Check: 6y - 2y + 5 = 17
6(3) - 2(3) + 5 = 17
18 - 6 + 5 = 17
12 + 5 = 17
Sample 4
Nina read 25 pages of a 175-page book. Nina now plans to read 15
pages a day. The equation 25 + 15x = 175 represents how many days it will take
Nina to read the rest of the book. Write the steps that can be used to solve the
equation.
25 + 15x = 175 Write the equation.
25 + 15x = 175
-25
= -25 Subtraction Property of Equality.
15x = 150 Simplify.
15x = 150
15x = 15 Division Property of Equality.
x = 10 Simplify.
To solve the equation, first subtract 25 and then divide by 15.
CHECK: 25 + 15x = 175 Write the equation.
25 + 15(10) = 175 Substitute the solution for x.
25 + 150 = 175 Multiply.
175 = 175 Add.