Question

Which of the following equations has a different value of x than the others?(1 point) Responses x + 9/8 = 7/4 x plus Start Fraction 9 over 8 End Fraction equals Start Fraction 7 over 4 End Fraction x − 0.025 = 0.6 x minus 0.025 equals 0.6 x − 7/8 = −3/2 x minus Start Fraction 7 over 8 End Fraction equals negative Start Fraction 3 over 2 End Fraction x + 0.875 = 1.5

Answer 1

To determine which equation has a different value of \( x \), we can solve each equation for \( x \):

1. **Equation:** \( x + \frac{9}{8} = \frac{7}{4} \)

Subtract \( \frac{9}{8} \) from both sides:
\[
x = \frac{7}{4} - \frac{9}{8}
\]
Convert \( \frac{7}{4} \) to eighths:
\[
\frac{7}{4} = \frac{14}{8}
\]
Thus,
\[
x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8}
\]

2. **Equation:** \( x - 0.025 = 0.6 \)

Add \( 0.025 \) to both sides:
\[
x = 0.6 + 0.025 = 0.625
\]

3. **Equation:** \( x - \frac{7}{8} = -\frac{3}{2} \)

Add \( \frac{7}{8} \) to both sides:
\[
x = -\frac{3}{2} + \frac{7}{8}
\]
Convert \( -\frac{3}{2} \) to eighths:
\[
-\frac{3}{2} = -\frac{12}{8}
\]
Thus,
\[
x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8}
\]

4. **Equation:** \( x + 0.875 = 1.5 \)

Subtract \( 0.875 \) from both sides:
\[
x = 1.5 - 0.875 = 0.625
\]

Now, we summarize the values of \( x \) obtained from each equation:

1. \( x = \frac{5}{8} \) (Equation 1)
2. \( x = 0.625 \) (Equation 2)
3. \( x = -\frac{5}{8} \) (Equation 3)
4. \( x = 0.625 \) (Equation 4)

From these results, we see that Equation 3 has a different value of \( x \) (which is \( -\frac{5}{8} \)) compared to the values from Equations 1, 2, and 4.

So, the answer is **Equation 3: \( x - \frac{7}{8} = -\frac{3}{2} \)** has a different value of \( x \).