Question

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

A. The equation has only one solution.
B. The equation has no solutions.
C. The equation has infinitely many solutions.
D. The equation's only solution is x = -17.
E. The equation is solved by all numbers less than 17.

Answer 1

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 \(x = -17\).**