Question

Q21 Determine whether the following linear equations have the same solution set.
4x + 10 = 34
2(x + 5) + 12 = 38

Answer 1

To determine whether the two linear equations have the same solution set, we will solve both equations and compare their solutions.

1. **First Equation:**
\[
4x + 10 = 34
\]
Subtract 10 from both sides:
\[
4x = 34 - 10
\]
\[
4x = 24
\]
Now divide both sides by 4:
\[
x = \frac{24}{4} = 6
\]

2. **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:
\[
2x = 38 - 22
\]
\[
2x = 16
\]
Now divide both sides by 2:
\[
x = \frac{16}{2} = 8
\]

3. **Comparing Solutions:**
- The solution for the first equation is \( x = 6 \).
- The solution for the second equation is \( x = 8 \).

Since the solutions are different, we conclude that the two linear equations do not have the same solution set.