Question

Solve for x:
square root of, 3, x, minus, 15, end square root, minus, 13, equals, minus, 10
3x−15
​
−13=
−10

Answer 1

To solve the equation

\[
\sqrt{3x - 15} - 13 = -10,
\]

we first isolate the square root term. We can do this by adding 13 to both sides:

\[
\sqrt{3x - 15} = -10 + 13.
\]

This simplifies to:

\[
\sqrt{3x - 15} = 3.
\]

Next, we square both sides to eliminate the square root:

\[
3x - 15 = 3^2.
\]

This simplifies to:

\[
3x - 15 = 9.
\]

Now, add 15 to both sides:

\[
3x = 9 + 15.
\]

This simplifies to:

\[
3x = 24.
\]

Finally, divide both sides by 3:

\[
x = \frac{24}{3} = 8.
\]

Thus, the solution is

\[
\boxed{8}.
\]

To verify, we can substitute \( x = 8 \) back into the original equation:

\[
\sqrt{3(8) - 15} - 13 = -10.
\]

Calculating inside the square root:

\[
3(8) - 15 = 24 - 15 = 9,
\]

so we have:

\[
\sqrt{9} - 13 = -10.
\]

This simplifies to:

\[
3 - 13 = -10,
\]

which is true. Therefore, the solution \( x = 8 \) is correct.