Which of the following is the set of real values of x that satisfies the inequality \frac{… — JAMB UTME

Which of the following is the set of real values of $x$ that satisfies the inequality $\frac{3 - x}{4} \le \frac{2x + 5}{3}$ ?

The set of real values of

x

that satisfies the inequality is

x \ge -1

Multiplying through by 12 gives

9 - 3x \le 8x + 20

. Grouping terms results in

-11x \le 11

. Dividing by

-11

requires reversing the inequality sign from

\le

\ge

, giving the solution

x \ge -1

Clear the denominators by multiplying both sides of the inequality by the lowest common multiple, 12.

3(3 - x) \le 4(2x + 5)

Eliminating fractions simplifies the algebraic expression.

Expand both sides by distributing the multipliers.

9 - 3x \le 8x + 20

Prepares terms for grouping variables on one side and constants on the other.

Collect all terms containing

x

on the left side and constant terms on the right side.

-3x - 8x \le 20 - 9 \implies -11x \le 11

Isolates the linear variable term.

Divide both sides by

-11

and flip the inequality sign.

x \ge -1

Dividing or multiplying an inequality by a negative number reverses the direction of the inequality sign.

Linear Inequalities and Reversing Inequality Sign on Division by Negative Numbers

Question