Question

Which of the following equations has a solution different from the rest?

1/2x -3 = 1/2

3/4x + 5 = -1/4

Answer 1

To determine which equation has a solution different from the rest, we need to solve both equations for \(x\).

1. For the first equation:
\[
\frac{1}{2}x - 3 = \frac{1}{2}
\]

Add 3 to both sides:
\[
\frac{1}{2}x = \frac{1}{2} + 3
\]
\[
\frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2}
\]

Now, multiply both sides by 2 to solve for \(x\):
\[
x = 7
\]

2. For the second equation:
\[
\frac{3}{4}x + 5 = -\frac{1}{4}
\]

Subtract 5 from both sides:
\[
\frac{3}{4}x = -\frac{1}{4} - 5
\]
\[
\frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} = -\frac{21}{4}
\]

Now, multiply both sides by \(\frac{4}{3}\) to solve for \(x\):
\[
x = -\frac{21}{4} \times \frac{4}{3} = -\frac{21}{3} = -7
\]

Now we summarize the solutions:
- First equation: \(x = 7\)
- Second equation: \(x = -7\)

Since the solutions are \(7\) and \(-7\), the equation that has a solution different from the other is the second equation:
\[
\frac{3}{4}x + 5 = -\frac{1}{4}
\]