Solving Compound Inequalities

a

When an inequality is multiplied or divided by a negative number, the inequality symbol must be flipped. This has not been done in the last step. $\begin{aligned} \text{-}4x < 8 \\ x < \text{-}2 \end{aligned}$ Ron-Jon divided both sides with $\text{-}4$ but he forgot to flip the sign.

b

Let's start from the beginning. Remember the rule for inequalities when multiplying or dividing by a negative.

13x\lt 17x+8

SubIneq

\text{LHS}-17x\lt\text{RHS}-17x

\text{-}4x\lt 8

DivNegIneqDivide by

\text{-}4

and flip inequality sign

x\gt \text{-}2

The inequality is, therefore, true if

x \gt \text{-}2.

Ron-Jon's solutions should have been as follows.

inequality that has been solved incorrectly

Solving Compound Inequalities 1.10 - Solution