Question

solve for all values of x in simplest form.
2 - 4|7 + 5x| = -26

Explanation:

Step1: Isolate the absolute value term

Subtract 2 from both sides:
$2 - 4|7+5x| - 2 = -26 - 2$
$-4|7+5x| = -28$

Step2: Solve for the absolute value

Divide both sides by -4:
$\frac{-4|7+5x|}{-4} = \frac{-28}{-4}$
$|7+5x| = 7$

Step3: Split into two linear equations

Absolute value equals 7 means two cases:
$7+5x = 7$ or $7+5x = -7$

Step4: Solve first linear equation

Subtract 7, then divide by 5:
$5x = 7 - 7$
$5x = 0$
$x = \frac{0}{5} = 0$

Step5: Solve second linear equation

Subtract 7, then divide by 5:
$5x = -7 - 7$
$5x = -14$
$x = \frac{-14}{5}$

Answer:

$x = 0$ and $x = -\frac{14}{5}$