Answer to Question #120642 in Algebra for usman

Question

Find all values of satisfying the inequality \\(-11\\leq 4-3x\\leq 28\\)

Answer 1

Given $-11 \leq 4-3x \leq 28$.

So, $-11 \leq 4-3x \implies -11-4\leq -3x \implies -15 \leq -3x \implies 5 \geq x$ .

And, $4-3x \leq 28 \implies -3x\leq 28-4 \implies -3x\leq24 \implies x \geq -8$ .

Hence, $-8\leq x\leq 5 \implies x\in[-8,5].$