Kerala KEAM 5 June 2024 Solved Paper

We are given the inequality: $$| 3x - 4 | \leq 5.$$By the definition of absolute value, we know that: $$| A | \leq B implies -B \leq A \leq B.$$Thus, we can rewrite the inequality as: $$-5 \leq 3x - 4 \leq 5.$$Step 1: Solve the inequalityAdd 4 to all parts of the inequality to isolate the term with $x$: $$-5 + 4 \leq 3x \leq 5 + 4 -1 \leq 3x \leq 9.$$Step 2: Divide by 3 to solve for $x$ $$\frac{-1}{3} \leq x \leq \frac{9}{3} -\frac{1}{3} \leq x \leq 3.$$Thus, the solution to the inequality is: $$x \in \left[ -\frac{1}{3}, 3 \right].$$Therefore, the correct answer is option (A), $\left[ -\frac{1}{3}, 3 \right]$.Quick Tip: For inequalities involving absolute values, isolate the expression inside the absolute value, remove the absolute value, and then solve the resulting compound inequality. Remember to consider both the positive and negative cases.