AnswersAZ-Algebra 1A MA101Solving Linear Equations: Variables on Both Sides

Solving Linear Equations: Variables on Both Sides Answers

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Use properties to rewrite the given equation. Which equations have the same solution as the equation x + + x = – xSelect three options.x + = – x18x + 20 + 30x = 15 – 6x18x + 20 + x = 15 – 6x24x + 30x = –512x + 30x = –5

Question illustration
A
x + = – x
Option A
B
18x + 20 + 30x = 15 – 6x
C
18x + 20 + x = 15 – 6x
D
24x + 30x = –5
E
12x + 30x = –5
2
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What is the solution to the linear equation?4b + 6 = 2 – b + 4

A
b = –2
B
b = 0
C
b = 4
D
b = 6
3

Which step could be used to help isolate the variable in the following equation?5.6j – 0.12 = 4 + 1.1j

A
Subtract 0.12 from both sides.
B
Subtract 5.6 from both sides.
C
Subtract 4j from both sides.
D
Subtract 1.1j from both sides.
4

Which number can each term of the equation be multiplied by to eliminate the fractions before solving?6 – x + = x + 5

Question illustration
A
2
B
3
C
6
D
12
5

Solve the equation.–3x + 1 + 10x = x + 4

A
x =
Option A
B
x =
Option B
C
x = 12
D
x = 18
6

Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month.

A
112 – 25m + 45 = 50 – 60m
B
112 + 25 + 45m = 50m + 60
C
112 + 25 – 45m = –50m + 60
D
112 + 25m + 45 = 50 + 60m
7

The International Business Club starts the school year with $250.50 in their account. They spend $35 each month on activities. The Future Agricultural Leaders Club starts with $300 and spends $45.25 each month.

A
250.5 + 35m = 300 + 45.25m
B
250.5 – 35m = 300 – 45.25m
C
250.5m – 35 = 300m – 45.25
D
250.5m + 35 = 300m + 45.25
8

What is the justification for the step taken from line 2 to line 3?

Question illustration
A
the subtraction property of equality
B
the multiplication property of equality
C
combining like terms on one side of the equation
D
the distributive property
9

What is the solution to the linear equation?d – 10 – 2d + 7 = 8 + d – 10 – 3d

A
d = –5
B
d = –1
C
d = 1
D
d = 5
10

What is the solution to the linear equation?x – = + x

Question illustration
A
x = –5
B
x = –
Option B
C
x =
Option C
D
x = 5

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