-5 + x - 2 = 3x + 10 - xWhich of the following statements correctly describe the solution(s) of the equation above? Select the 2 that apply.

Let's solve the equation step by step:

\[ -5 + x - 2 = 3x + 10 - x \]

First, simplify both sides:

\[ -7 + x = 2x + 10 \]

Next, isolate \(x\) by getting all terms involving \(x\) on one side and constant terms on the other side. Subtract \(x\) from both sides:

\[ -7 = 2x - x + 10 \]

This simplifies to:

\[ -7 = x + 10 \]

Now, subtract 10 from both sides:

\[ -7 - 10 = x \]

So:

\[ x = -17 \]

Now, let's evaluate the provided statements:

A. The equation has only one solution.
This is true because we found a single value for \(x\).

B. The equation has no solutions.
This is false because we have found a solution.

C. The equation has infinitely many solutions.
This is false because there is only one solution.

D. The equation's only solution is \(x = -17\).
This is true because we've determined that the solution is indeed \(x = -17\).

E. The equation is solved by all numbers less than 17.
This is false since \(x = -17\) is the only solution.

Thus, the two correct statements are:

A. The equation has only one solution.
D. The equation's only solution is \(x = -17\).