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].
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].