To solve the exercise you can use this property of the absolute value:
[tex]|x|\le a=-a\le x\le a[/tex]
So, in this case, you have
[tex]|6+9x|\le24=-24\le6+9x\le24[/tex]
Then
[tex]\begin{gathered} -24\le6+9x \\ \text{ and} \\ 6+9x\le24 \end{gathered}[/tex]
To solve the first part you can proceed like this:
[tex]\begin{gathered} -24\le6+9x \\ \text{ Subtract 6 from both sides of the inequality} \\ -24-6\le6+9x-6 \\ -30\le9x \\ \text{ Divide by 9 from both sides of the inequality} \\ -\frac{30}{9}\le\frac{9x}{9} \\ -\frac{30}{9}\le x \\ \text{ Simplify} \\ -\frac{3\cdot10}{3\cdot3}\le x \\ -\frac{10}{3}\le x \end{gathered}[/tex]
To solve the second part you can proceed like this:
[tex]\begin{gathered} 6+9x\le24 \\ \text{ Subtract 6 from both sides of the inequality} \\ 6+9x-6\le24-6 \\ 9x\le18 \\ \text{ Divide by 9 from both sides of the inequality} \\ \frac{9x}{9}\le\frac{18}{9} \\ x\le2 \end{gathered}[/tex]
Therefore, the solution to the inequality will be
[tex]-\frac{10}{3}\le x\le2[/tex]
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