Let's solve each equation for \( x \) and see which one has a different value.
A. \( x + \frac{9}{8} = \frac{7}{4} \)
To isolate \( x \): \[ x = \frac{7}{4} - \frac{9}{8} \]
Convert \(\frac{7}{4}\) to eighths: \[ \frac{7}{4} = \frac{14}{8} \]
So: \[ x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \]
B. \( x + 0.875 = 1.5 \)
To isolate \( x \): \[ x = 1.5 - 0.875 \] \[ x = 0.625 \]
C. \( x - \frac{7}{8} = -\frac{3}{2} \)
To isolate \( x \): \[ x = -\frac{3}{2} + \frac{7}{8} \]
Convert \(-\frac{3}{2}\) to eighths: \[ -\frac{3}{2} = -\frac{12}{8} \]
So: \[ x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \]
D. \( x - 0.025 = 0.6 \)
To isolate \( x \): \[ x = 0.6 + 0.025 \] \[ x = 0.625 \]
Now, summarizing the results:
- \( A: x = \frac{5}{8} \)
- \( B: x = 0.625 \)
- \( C: x = -\frac{5}{8} \)
- \( D: x = 0.625 \)
From this, we see that:
- Equations B and D yield the same value of \( x = 0.625 \).
- Equation A gives \( \frac{5}{8} \), which is equivalent to 0.625.
- Equation C gives \( x = -\frac{5}{8} \), which is \(-0.625\).
Thus, the equation with a different value of \( x \) is: C: x - \frac{7}{8} = -\frac{3}{2}.