Question

Solve the inequality in express your answer in interval notation used decimal form for numerical values

Answer 1

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

STEP 1: Write the given inequality

`-12<3z-9\leq18`

STEP 2: Simplify the inequality

`\begin{gathered} -12\lt3z-9\leq18 \\ \mathrm{If}\:a<u>-1 \end{gathered}`

Solve the other part

`\begin{gathered} 3z-9\leq18 \\ 3z\leq18+9 \\ 3z\leq27 \\ z\leq(27)/(3)=9 \\ z\leq9 \end{gathered}`

STEP 3: Combine the intervals

`z>-1\quad \mathrm{and}\quad \:z\le \:9`

STEP 4: Merge the overlapping intervals

`-1<strong>STEP 5: Give the answer in interval notation</strong><p><strong>Hence, the final answer will be given as:</strong></p>[tex](-1,9]`