Solve the following compound inequality and present the solution set both on a number…

MATHEMATICS · Multi-part · AoPS · Mathematics · Introduction to Inequalities · Introduction to Inequalities

Problem

Solve the following compound inequality and present the solution set both on a number line and in interval notation: (i)

-4 < 2(3 - x) \le 5 - \dfrac{x}{2}

(ii) Show each algebraic step used to isolate

x

, clearly indicating where (if anywhere) the inequality symbol changes direction. (iii) Verify the final answer by testing one value of

x

from within the obtained solution interval and one value outside it.