Question

Determine whether the following linear equations have the same solution set.

4x + 10 = 34
2(x + 5) + 12 = 38
(1 point)
Responses

Yes
Yes

No

Answer 1

To determine if the two linear equations have the same solution set, we can solve each equation separately and compare their solutions.

1. Solve the first equation:
\[
4x + 10 = 34
\]
Subtract 10 from both sides:
\[
4x = 34 - 10
\]
\[
4x = 24
\]
Divide both sides by 4:
\[
x = \frac{24}{4} = 6
\]

2. Solve the second equation:
\[
2(x + 5) + 12 = 38
\]
First, distribute the 2:
\[
2x + 10 + 12 = 38
\]
Combine like terms:
\[
2x + 22 = 38
\]
Subtract 22 from both sides:
\[
2x = 38 - 22
\]
\[
2x = 16
\]
Divide both sides by 2:
\[
x = \frac{16}{2} = 8
\]

Now we have the solutions:
- The first equation \(4x + 10 = 34\) has the solution \(x = 6\).
- The second equation \(2(x + 5) + 12 = 38\) has the solution \(x = 8\).

Since \(x = 6\) and \(x = 8\) are not the same, the linear equations do not have the same solution set.

Therefore, the answer is **No**.