To find which equation has a different value of \( x \), we will solve each equation for \( x \).
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Equation 1: \( X + 0.875 = 1.5 \) \[ X = 1.5 - 0.875 = 0.625 \]
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Equation 2: \( X - 0.025 = 0.6 \) \[ X = 0.6 + 0.025 = 0.625 \]
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Equation 3: \( X + 9.8 = \frac{7}{4} \) \[ X = \frac{7}{4} - 9.8 \] First, convert 9.8 to a fraction: \[ 9.8 = \frac{98}{10} = \frac{49}{5} \] Now convert \(\frac{7}{4}\) to a common denominator: \[ \frac{7}{4} = \frac{35}{20} \quad \text{and} \quad \frac{49}{5} = \frac{196}{20} \] Now, substitute back: \[ X = \frac{35}{20} - \frac{196}{20} = \frac{35 - 196}{20} = \frac{-161}{20} = -8.05 \]
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Equation 4: \( X - \frac{7}{8} = - \frac{3}{2} \) \[ X = -\frac{3}{2} + \frac{7}{8} \] Convert \(-\frac{3}{2}\) to a fraction with a common denominator of 8: \[ -\frac{3}{2} = -\frac{12}{8} \] Now calculate \(X\): \[ X = -\frac{12}{8} + \frac{7}{8} = \frac{-12 + 7}{8} = \frac{-5}{8} \]
Now we have the values of \( x \) for each equation:
- From Equation 1: \( x = 0.625 \)
- From Equation 2: \( x = 0.625 \)
- From Equation 3: \( x = -8.05 \)
- From Equation 4: \( x = -\frac{5}{8} \)
Comparing these, we see that:
- Equation 1 and Equation 2 both give \( x = 0.625 \).
- Equation 3 gives \( x = -8.05 \).
- Equation 4 gives \( x = -\frac{5}{8} = -0.625 \).
Thus, the equation that has a different value of \( x \) than the others is:
Equation 3: \( X + 9.8 = \frac{7}{4} \) (which leads to \( x = -8.05 \)).