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 – 3B
3x < 8x – 3C
5 < 10x – 3D
2 – 2x < 8x3
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
A
x < 5B
–6x – 5 < 10 – xC
–6x + 15 < 10 – 5xD
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.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.
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≤−2B
x≥−2C
x≤3D
x≥37
Which number line represents the solution set for the inequality –x ≥ 4?
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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