What is the correct solution set for the inequality shown below? 4(x - 1) - 2(x + 3) \geq … — Armed Services Vocational Aptitude Battery (ASVAB)

What is the correct solution set for the inequality shown below?

4(x - 1) - 2(x + 3) \geq 5x + 2

$x \leq -4$ Answer
B
$x \geq -4$
C
$x \leq 0$
D
$x \leq 4$

Answer

The correct solution set is

x \leq -4

The correct answer is derived by carefully distributing the coefficients, combining like terms, isolating the variable

x

, and applying the rule to reverse the inequality symbol when dividing by a negative number.

Step-by-Step Solution

Distribute the values

4

and

-2

into their respective parentheses on the left side.

4x - 4 - 2x - 6 \geq 5x + 2

This step removes the parentheses and prepares the terms for grouping.

Combine the like terms on the left side of the inequality.

2x - 10 \geq 5x + 2

Simplifying expressions on each side makes it easier to isolate the variable.

Subtract

5x

from both sides, and add

10

to both sides.

-3x \geq 12

This moves all variable terms to the left side and all constant terms to the right side.

Divide both sides by

-3

and reverse the direction of the inequality symbol.

x \leq -4

When dividing or multiplying an inequality by a negative number, the relationship between the two sides inverses, so the sign must be flipped.

Key Concept

Solving one-variable linear inequalities requires isolating the variable using inverse operations, and reversing the inequality symbol when multiplying or dividing by a negative number.

Question

Answer

Step-by-Step Solution

Key Concept

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