Question

solve the inequality: $3|m + 7| + 9 < 30$ options: $m > 0$ or $m < -14$, $m < 0$, $-8 < m < -6$, $-14 < m < 0$

Explanation:

Step1: Isolate the absolute value term

Subtract 9 from both sides.
$3|m + 7| + 9 - 9 < 30 - 9$
$3|m + 7| < 21$

Step2: Simplify the inequality

Divide both sides by 3.
$\frac{3|m + 7|}{3} < \frac{21}{3}$
$|m + 7| < 7$

Step3: Rewrite without absolute value

For $|A| < b$, $-b < A < b$.
$-7 < m + 7 < 7$

Step4: Solve for m

Subtract 7 from all parts.
$-7 - 7 < m + 7 - 7 < 7 - 7$
$-14 < m < 0$

Answer:

$-14 < m < 0$