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

Solving Linear Equations: Variables on Both Sides Answers

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Which number can each term of the equation be multiplied by to eliminate the decimals before solving?–m + 0.02 + 2.1m = –1.45 – 4.81m

A
0.01
B
0.1
C
10
D
100
2
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Which number can each term of the equation be multiplied by to eliminate the fractions before solving?m – = 2 + m

Question illustration
A
2
B
3
C
4
D
5
3

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
4

Solve the equation.y + 6 = –3y + 26

A
y = –8
B
y = –5
C
y = 5
D
y = 8
5

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
6

What is the solution to the linear equation?2.8y + 6 + 0.2y = 5y – 14

A
y = –10
B
y = –1
C
y = 1
D
y = 10
7

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
8

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
9

Use properties to rewrite the given equation. Which equations have the same solution as the equation x + + x = – xSelect three options.

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
10

The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year.

A
0.05 – 0.1y = 0.12 – 0.06y
B
0.05y + 0.1 = 0.12y + 0.06
C
0.05 + 0.1y = 0.12 + 0.06y
D
0.05y – 0.1 = 0.12y – 0.06
11

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
12

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

Question illustration
A
x =
Option A
B
x =
Option B
C
x = 12
D
x = 18
13

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
14

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

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