Question

solve for all values of a in simplest form. |-3a + 8| = 11

Explanation:

Step1: Split absolute value equation

For $|A|=B$, solve $A=B$ and $A=-B$:

1. $-3a + 8 = 11$
2. $-3a + 8 = -11$

Step2: Solve first equation

Isolate $a$:
$-3a = 11 - 8$
$-3a = 3$
$a = \frac{3}{-3} = -1$

Step3: Solve second equation

Isolate $a$:
$-3a = -11 - 8$
$-3a = -19$
$a = \frac{-19}{-3} = \frac{19}{3}$

Answer:

$a = -1$ and $a = \frac{19}{3}$