AnswersAZ-Intermediate Algebra A MA311Solving Linear Equations: Variable on One Side

Solving One-Variable Inequalities Answers

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Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x?

A
Distribute –4 to get –8x + 4 > 5 – 3x.
B
Distribute –4 to get –8x – 1 > 5 – 3x.
C
Subtract 2x from both sides of the inequality.
D
Add 1 to both sides of the inequality.
2
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Which is a correct first step in solving 5 – 2x < 8x – 3?

A
5 < 6x – 3
B
3x < 8x – 3
C
5 < 10x – 3
D
2 – 2x < 8x
3

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

Question illustration
A
x < 5
B
–6x – 5 < 10 – x
C
–6x + 15 < 10 – 5x
D
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Option D
E
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Option E
4

What value of x is in the solution set of the inequality 8x – 6 > 12 + 2x?

A
–1
B
0
C
3
D
5
5

Step 1: Subtract 3 from both sides of the inequality.Step 2: __________Step 3: Divide both sides of the inequality by the coefficient of x.

A
Add 2x to both sides of the inequality.
B
Subtract 8x from both sides of the inequality.
C
Subtract 2x from both sides of the inequality.
D
Add 8x to both sides of the inequality.
6

Solve the inequality.2(4+2x)≥5x+5

A
x≤−2
B
x≥−2
C
x≤3
D
x≥3
7

Which number line represents the solution set for the inequality –x ≥ 4?

Question illustration
A
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the left.
Option A
B
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the left.
Option B
C
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the right.
Option C
D
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the right.
Option D
8

Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?

A
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
Option A
B
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.
Option B
C
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the left.
Option C
D
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
Option D
9

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

A
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
Option A
B
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
Option B
C
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
Option C
D
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Option D
10

What value of x is in the solution set of the inequality 4x – 12 ≤ 16 + 8x?

A
–10
B
–9
C
–8
D
–7

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