Question

solve for x.
$2\sqrt{5x - 4} - 2 = 6$
a. $x=4$
b. $x=1.6$
c. $x=13$
d. $x=7$

Explanation:

Step1: Isolate the radical term

Add 2 to both sides:
$2\sqrt{5x-4}=6+2$
$2\sqrt{5x-4}=8$

Step2: Simplify the radical coefficient

Divide both sides by 2:
$\sqrt{5x-4}=\frac{8}{2}$
$\sqrt{5x-4}=4$

Step3: Eliminate the square root

Square both sides:
$(\sqrt{5x-4})^2=4^2$
$5x-4=16$

Step4: Solve for x

Add 4 to both sides, then divide by 5:
$5x=16+4$
$5x=20$
$x=\frac{20}{5}$

Answer:

a. x=4