Which of the following represents the solution set of real values of x satisfying the ineq… — JAMB UTME

Which of the following represents the solution set of real values of $x$ satisfying the inequality $4(1 - x) \le 3(x + 6)$ ?

The set of real values satisfying the inequality is

x \ge -2

Expanding the given inequality yields

4 - 4x \le 3x + 18

. Subtracting

3x

and

4

from both sides gives

-7x \le 14

. When dividing both sides by

-7

, the inequality sign must reverse direction, yielding

x \ge -2

Expand both sides of the inequality

4 - 4x \le 3x + 18

Remove brackets to group like terms.

Rearrange terms by moving variable terms to the left side and constant terms to the right side

-4x - 3x \le 18 - 4 \implies -7x \le 14

Isolate the term containing the variable

x

Divide both sides by

-7

and reverse the inequality sign

x \ge -2

Dividing or multiplying an inequality by a negative number flips the direction of the inequality symbol.

Solving linear inequalities involving bracket expansion and division by negative numbers

Question