Solve the following inequality for x: -2x + 6 \leq 14 Which of the following is the correc… — Armed Services Vocational Aptitude Battery (ASVAB)

Solve the following inequality for $x$ :

-2x + 6 \leq 14

Which of the following is the correct solution?

$x \geq -4$ Answer
B
$x \leq -4$
C
$x \geq 4$
D
$x \leq -10$

Answer

The correct solution is

x \geq -4

The correct answer is found by subtracting 6 from 14 to get 8, and then dividing 8 by -2. Because we divided by a negative number, the less than or equal to symbol (

\leq

) must flip to a greater than or equal to symbol (

\geq

), yielding

x \geq -4

Step-by-Step Solution

Subtract 6 from both sides of the inequality to isolate the variable term.

-2x \leq 14 - 6

-2x \leq 8

This is the first step in using inverse operations to isolate

x

Divide both sides by

-2

and reverse the inequality symbol.

x \geq 8 \div (-2)

x \geq -4

When multiplying or dividing an inequality by a negative number, the direction of the inequality sign must be flipped.

Key Concept

Solving One-Variable Inequalities

Question

Answer

Step-by-Step Solution

Key Concept

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