Question

Solve the inequality. Express you answer in interval notation. -3(x + 2) > 15 or x-3< -1

Answer 1

SOLUTION

We are told to solve the inequality

$-3\mleft(x+2\mright)>15\text{ or }x-3<-1​$

This becomes

$\begin{gathered} -3(x+2)>15\text{ or }x-3<-1​ \\ -3x-6>15\text{ or }x<2 \\ -3x>11\text{ or }x<2 \\ x<-\frac{11}{3}\text{ or }x<2 \end{gathered}$

In interval notation, this becomes

$(-\infty,-\frac{11}{3})\cup(-\infty,2)$