Respuesta :

SOLUTION

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

STEP 1: Write the given inequality

[tex]-12<3z-9\leq18[/tex]

STEP 2: Simplify the inequality

[tex]\begin{gathered} -12\lt3z-9\leq18 \\ \mathrm{If}\:a-1 \end{gathered}[/tex]

Solve the other part

[tex]\begin{gathered} 3z-9\leq18 \\ 3z\leq18+9 \\ 3z\leq27 \\ z\leq\frac{27}{3}=9 \\ z\leq9 \end{gathered}[/tex]

STEP 3: Combine the intervals

[tex]z>-1\quad \mathrm{and}\quad \:z\le \:9[/tex]

STEP 4: Merge the overlapping intervals

[tex]-1STEP 5: Give the answer in interval notation

Hence, the final answer will be given as:

[tex](-1,9][/tex]

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