Question

-12<-3x+9<24.solve this.

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given inequality expression

$12<-3x+9<24$

STEP 2: Simplify the inequality

$\begin{gathered} -12<-3x+9<24 \\ \mathrm{If}\:aSolving the two inequalities in parts will be:[tex]\begin{gathered} -12<-3x+9 \\ -12-9<-3x \\ -21<-3x \\ -\frac{21}{-3}>x \\ 7>x \\ x<7 \end{gathered}$

For the second part

$\begin{gathered} -3x+9<24 \\ -3x<24-9 \\ -3x<15 \\ x>\frac{15}{-3} \\ x>-5 \end{gathered}$

Combine the two results to have:

[tex]\begin{gathered} x<7\quad \mathrm{and}\quad \:x>-5 \\ overlapping\text{ }merging\text{ }intervals \\ -5Hence, the final solution will be:[tex]-5