Question

question
solve for x:
\sqrt{8x - 48} - 15 = -11
answer attempt 1 out of 10
x =
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Explanation:

Step1: Isolate the square root term

Add 15 to both sides of the equation $\sqrt{8x - 48}-15=-11$ to get $\sqrt{8x - 48}=-11 + 15$.
Simplify the right - hand side: $\sqrt{8x - 48}=4$.

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{8x - 48}=4$ to obtain $(\sqrt{8x - 48})^2=4^2$.
Using the property $(\sqrt{a})^2=a$ (for $a\geq0$), we have $8x-48 = 16$.

Step3: Solve for x

Add 48 to both sides of the equation $8x-48 = 16$: $8x=16 + 48$.
Simplify the right - hand side: $8x=64$.
Divide both sides by 8: $x=\frac{64}{8}=8$.

Step4: Check the solution

Substitute $x = 8$ into the original equation $\sqrt{8x-48}-15$.
First, calculate $8x-48$ when $x = 8$: $8\times8-48=64 - 48 = 16$.
Then $\sqrt{16}-15=4 - 15=-11$, which is equal to the right - hand side of the original equation. So $x = 8$ is a valid solution.

Answer:

$x = 8$