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

Question

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.