Q.Solve the compound inequality $-5 \le \dfrac{3x+2}{4} < 4$ for real $x$, and write the solution as an interval.

Solving a linear inequality algebraically isolates the variable using the same style of operations as solving an equation, with one crucial difference: adding or subtracting any quantity, or multiplying or dividing by a positive number, keeps the inequality's direction unchanged, but multiplying or dividing by a negative number reverses it. This follows directly from the fact that a positive number times a positive number is positive: if $a<b$ then $b-a>0$, and multipl …