AnswersCommon Core Algebra I A-ICSolving One-Variable Inequalities

Solving One-Variable Inequalities Answers

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What value of x is in the solution set of the inequality 2(3x – 1) ≥ 4x – 6?

A
–10
B
–5
C
–3
D
–1
2
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Which number line represents the solution set for the inequality –4(x + 3) ≤ –2 – 2x?

A
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
Option A
B
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the right.
Option B
C
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the left.
Option C
D
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
Option D
3

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

A
–1
B
0
C
3
D
5
4

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
5

Solve the inequality.2(4+2x)≥5x+5

A
x≤−2
B
x≥−2
C
x≤3
D
x≥3
6

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
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

What value of x is in the solution set of the inequality –5x – 15 > 10 + 20x?

A
–2
B
–1
C
0
D
1
9

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.
10

What value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18?

A
–4
B
–3
C
–2
D
–1

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