Find the set of real values of x that satisfies the inequality \frac{5 - 2x}{3} \ge x - 5. — JAMB UTME

Find the set of real values of $x$ that satisfies the inequality $\frac{5 - 2x}{3} \ge x - 5$ .

The set of real values satisfying the inequality is

x \le 4

Multiplying through by

3

yields

5 - 2x \ge 3x - 15

. Rearranging terms gives

-5x \ge -20

. Dividing both sides by

-5

requires flipping the inequality sign from

\ge

\le

, giving

x \le 4

Multiply both sides of the inequality by 3 to clear the fraction.

5 - 2x \ge 3(x - 5)

Eliminating the denominator simplifies the algebraic expression.

Expand the right-hand side and collect terms containing

x

on one side and constants on the other.

5 - 2x \ge 3x - 15 \implies -2x - 3x \ge -15 - 5 \implies -5x \ge -20

Group like terms to isolate the variable

x

Divide both sides by

-5

and reverse the inequality sign.

x \le \frac{-20}{-5} \implies x \le 4

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

Solving linear inequalities involving negative coefficient division

Question