Answer :

Let's solve the equation step by step:

The equation is:

[tex]\[
\sqrt{3x + 76} + 7 = 15
\][/tex]

Step 1: Isolate the square root term.

To do this, subtract 7 from both sides of the equation:

[tex]\[
\sqrt{3x + 76} = 15 - 7
\][/tex]

[tex]\[
\sqrt{3x + 76} = 8
\][/tex]

Step 2: Square both sides to eliminate the square root.

By squaring both sides, we get:

[tex]\[
(\sqrt{3x + 76})^2 = 8^2
\][/tex]

[tex]\[
3x + 76 = 64
\][/tex]

Step 3: Solve for [tex]\(x\)[/tex].

Subtract 76 from both sides:

[tex]\[
3x = 64 - 76
\][/tex]

[tex]\[
3x = -12
\][/tex]

Now, divide both sides by 3 to solve for [tex]\(x\)[/tex]:

[tex]\[
x = \frac{-12}{3}
\][/tex]

[tex]\[
x = -4
\][/tex]

So, the solution to the equation is [tex]\(x = -4\)[/tex].

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