Which of the following inequalities represents all real values of x that satisfy -3x + 14 … — GRE General Test

Which of the following inequalities represents all real values of $x$ that satisfy $-3x + 14 \le 2$ ?

x \ge 4

Subtracting 14 from both sides of

-3x + 14 \le 2

yields

-3x \le -12

. Dividing both sides by

-3

requires reversing the inequality sign from

\le

\ge

, giving

x \ge 4

. Thus, the inequality

x \ge 4

correctly represents all solution values.

Isolate the variable term on the left side of the inequality.

Subtract 14 from both sides:

-3x \le 2 - 14

, which simplifies to

-3x \le -12

To solve for

x

, constant terms must first be removed from the variable side using inverse operations.

Divide both sides by the coefficient of

x

and apply the inequality rule for negative multipliers.

Divide by

-3

and reverse the inequality sign:

x \ge \frac{-12}{-3}

, which simplifies to

x \ge 4

Dividing or multiplying an inequality by a negative quantity changes the direction of the inequality sign.

Solving linear inequalities with negative coefficients

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