Solving Linear Equations: Variable on One Side Answers

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Mustafa’s soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit?

5n – 300 = 1,500

5n + 300 = 1,500

5n – 200 + 100n = 1,500

5n – 100 – 200n = 1,500

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A number, n, is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of n?

3n – 15 + n = 101

3n + 15 + n = 101

3n – 15 – n = 101

3n + 15 – n = 101

What are the possible steps involved in solving the equation shown? Select three options.3.5 + 1.2(6.3 – 7x) = 9.38Add 3.5 and 1.2.Distribute 1.2 to 6.3 and –7x .Combine 6.3 and –7x .Combine 3.5 and 7.56.Subtract 11.06 from both sides.

Add 3.5 and 1.2.

Distribute 1.2 to 6.3 and –7x .

Combine 6.3 and –7x .

Combine 3.5 and 7.56.

Subtract 11.06 from both sides.

Sonji paid $25 for two scarves, which were different prices. When she got home she could not find the receipt. She remembered that one scarf cost $3 more than the other. What was the price of the more expensive scarf?

$11

$12

$13

$14

The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?

u = 0.25

u = 0.75

u = 1.1

u = 2.5

A coordinate grid with 2 lines. One line, labeled f(x) passing through (negative 3, 3), (0, 3), and the point (4, 3). The other line is labeled g(x) and passes through (negative 4, negative 3), (0, 0), and the point (4, 3).

x = −1

x = 0

x = 3

x = 4

A coordinate grid with 2 lines. One line, labeled f(x) passing through (negative 2, 4), (0, 2), and the point (1, 1). The other line is labeled g(x) and passes through (negative 3, negative 3), (0, 0) and the point (1, 1).

x = −1

x = 0

x = 1

x = 2

Rahul solved the equation 2(x – ) – x = . In which step did he use the addition property of equality?

Step 1

Step 2

Step 3

Step 4

The Allied Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?

1.95x + 2.50 = 27.46; Isaac traveled 15.4 miles.

1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.

2.50x + 1.95 = 27.46; Isaac traveled 11.8 miles.

2.50x + 1.95 = 27.46; Isaac traveled 10.2 miles.

Consider the functions shown on the graph.

0.0

0.5

1.5

3.0

A coordinate grid with 2 lines. One line, labeled f(x) passing through (negative 4, 3), the point (negative 2, 1) and (0, negative 1). The other line is labeled g(x) and passes through (negative 4, negative 1), the point (negative 2, 1) and (0, 3).

x = −3

x = −2

x = −1

x = 3

Consider the equation 3p – 7 + p = 13. What is the resulting equation after the first step in the solution?

p – 7 = 13 – 3p

2p – 7 = 13

3p – 7 = 13 – p

4p – 7 = 13

Sean began jogging to live a healthier lifestyle. On his first run, he ran one-half mile. He increased his workouts by adding two miles a month to his run. He wrote the equation f(x)= 0.5 + 2x to model his progress. The variable x represents the number of

miles he runs.

months he runs.

miles he ran the first day.

calories he burns.

Two functions are defined as shown.f(x) = x – 2g(x) = –1Which graph shows the input value for which f(x) = g(x)?

Option

Solve the equation.5x + 8 − 3x = −10

x = −9

x = −1

x = 1

x = 9

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Solving Linear Equations: Variable on One Side Answers

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