Question

$|8a + 10| + 3 < 25$

Explanation:

Step1: Isolate the absolute value

Subtract 3 from both sides.
$|8a + 10| < 25 - 3$
$|8a + 10| < 22$

Step2: Rewrite without absolute value

Convert to compound inequality.
$-22 < 8a + 10 < 22$

Step3: Subtract 10 from all parts

Isolate the term with $a$.
$-22 - 10 < 8a < 22 - 10$
$-32 < 8a < 12$

Step4: Divide by 8 to solve for $a$

Find the range of $a$.
$\frac{-32}{8} < a < \frac{12}{8}$
$-4 < a < \frac{3}{2}$

Answer:

$-4 < a < \frac{3}{2}$