Question

cubic and cube root functions and equations
what is the solution to the equation $sqrt{5x - 7} = sqrt{3x + 5}$?
$x = 12$
$x = 24$
$x = 1$
$x = 6$

Explanation:

Step1: Square both sides to eliminate roots

$$(\sqrt{5x - 7})^2 = (\sqrt{3x + 5})^2$$
$$5x - 7 = 3x + 5$$

Step2: Isolate x terms on one side

$$5x - 3x = 5 + 7$$
$$2x = 12$$

Step3: Solve for x

$$x = \frac{12}{2}$$
$$x = 6$$

Step4: Verify the solution

Substitute $x=6$ into original equation:
Left side: $\sqrt{5(6)-7}=\sqrt{30-7}=\sqrt{23}$
Right side: $\sqrt{3(6)+5}=\sqrt{18+5}=\sqrt{23}$
Both sides are equal, so solution is valid.

Answer:

$x=6$