Question

8.6 solve radical equations (homework)
score: 13/16 answered: 13/16
question 14
solve.
$(4a - 5)^{\frac{1}{3}}+10 = 5$
$a=$

Explanation:

Step1: Isolate the radical term

Subtract 10 from both sides of the equation.
$$(4a - 5)^{\frac{1}{3}}=5 - 10=- 5$$

Step2: Eliminate the cube - root

Cube both sides of the equation.
$$((4a - 5)^{\frac{1}{3}})^3=(-5)^3$$
Since $((x)^n)^m=x^{nm}$, we have $4a-5=-125$.

Step3: Solve for a

Add 5 to both sides: $4a=-125 + 5=-120$.
Then divide both sides by 4: $a=\frac{-120}{4}=-30$.

Answer:

$a = - 30$