Question

Solve the equation for x.

the square root of the quantity x plus 4 end quantity minus 7 equals 1

x = 4
x = 12
x = 60
x = 68

Answer 1

To solve the equation given, we start with:

\[
\sqrt{x + 4} - 7 = 1
\]

First, we will isolate the square root by adding 7 to both sides:

\[
\sqrt{x + 4} = 1 + 7
\]
\[
\sqrt{x + 4} = 8
\]

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

\[
(\sqrt{x + 4})^2 = 8^2
\]
\[
x + 4 = 64
\]

Now, we will solve for \( x \) by subtracting 4 from both sides:

\[
x = 64 - 4
\]
\[
x = 60
\]

Thus, the solution is:

\[
\boxed{60}
\]

Verifying our solution by substituting \( x = 60 \) back into the original equation:

\[
\sqrt{60 + 4} - 7 = 1
\]
\[
\sqrt{64} - 7 = 1
\]
\[
8 - 7 = 1
\]

This holds true, confirming that the solution \( x = 60 \) is correct.