Question

absolute value equations (basic) l2
this is the only question in this section
question
solve for all values of b in simplest form.
30 = |10 + 4b|
answer attempt 1 out of 3
additional solution no solution
b =

Explanation:

Step1: Set up two equations

Since $|x| = a$ ($a\geq0$) implies $x = a$ or $x=-a$, for $30 = |10 + 4b|$, we have $10 + 4b=30$ or $10 + 4b=-30$.

Step2: Solve the first equation

Solve $10 + 4b=30$. Subtract 10 from both sides: $4b=30 - 10=20$. Then divide both sides by 4: $b=\frac{20}{4}=5$.

Step3: Solve the second equation

Solve $10 + 4b=-30$. Subtract 10 from both sides: $4b=-30 - 10=-40$. Then divide both sides by 4: $b=\frac{-40}{4}=-10$.

Answer:

$b = 5$ or $b=-10$