Question

Solve and check the equation.
2 left parenthesis 3 minus 2 x right parenthesis equals 2 left parenthesis 2 x plus 5 right parenthesis
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Part 1
Select the correct choice below​ and, if​ necessary, fill in any answer box to complete your answer.
A.
The solution set is StartSet nothing EndSet
  
.
B.
The solution set is StartSet x| x is a real number EndSet.
C.
The solution set is empty set.

Answer 1

Let's solve the equation step by step:

Given equation:

\[
2(3 - 2x) = 2(2x + 5)
\]

1. Distribute on both sides:

\[
6 - 4x = 4x + 10
\]

2. Next, let's move all the terms involving \( x \) to one side and the constant terms to the other side. Adding \( 4x \) to both sides:

\[
6 = 4x + 4x + 10
\]

This simplifies to:

\[
6 = 8x + 10
\]

3. Now, subtract \( 10 \) from both sides:

\[
6 - 10 = 8x
\]

This gives:

\[
-4 = 8x
\]

4. Now, divide both sides by \( 8 \):

\[
x = -\frac{4}{8} = -\frac{1}{2}
\]

Now we found the value of \( x \).

### Checking the solution:
Substituting \( x = -\frac{1}{2} \) back into the original equation:

Left-hand side:

\[
2(3 - 2(-\frac{1}{2})) = 2(3 + 1) = 2(4) = 8
\]

Right-hand side:

\[
2(2(-\frac{1}{2}) + 5) = 2(-1 + 5) = 2(4) = 8
\]

Both sides are equal:

\[
8 = 8
\]

Thus, the solution is verified.

### Conclusion:
The solution set is:

\[
\text{The solution set is } \{ -\frac{1}{2} \}
\]

None of the options provided directly match with this result, but it does confirm that the answer is not nothing or the entire set of real numbers. Therefore, the closest correct interpretation is option A:

A. The solution set is StartSet nothing EndSet (if properly interpreted as \{-\frac{1}{2}\} being the actual value).

If you interpret options differently, please reach back for clearer ones.