Let's solve each equation step by step to find the value of \( x \) for each one:
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Equation: \( x - 78 = -32 \)
\[ x = -32 + 78 \] \[ x = 46 \]
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Equation: \( x - \frac{7}{8} = -\frac{3}{2} \)
First, convert \( -\frac{3}{2} \) to a fraction with a common denominator of 8: \[ -\frac{3}{2} = -\frac{12}{8} \] Now substitute: \[ x - \frac{7}{8} = -\frac{12}{8} \] \[ x = -\frac{12}{8} + \frac{7}{8} \] \[ x = -\frac{5}{8} \]
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Equation: \( x + 0.875 = 1.5 \)
Convert \( 0.875 \) to a fraction: \[ 0.875 = \frac{7}{8} \] Now substitute it into the equation: \[ x + \frac{7}{8} = 1.5 \] Converting \( 1.5 \) to a fraction: \[ 1.5 = \frac{3}{2} = \frac{12}{8} \] So: \[ x + \frac{7}{8} = \frac{12}{8} \] \[ x = \frac{12}{8} - \frac{7}{8} \] \[ x = \frac{5}{8} \]
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Equation: \( x + 98 = 74 \)
\[ x = 74 - 98 \] \[ x = -24 \]
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Equation: \( x - 0.025 = 0.6 \)
Convert \( 0.025 \) to a fraction: \[ 0.025 = \frac{25}{1000} = \frac{1}{40} \] Now substitute it into the equation: \[ x - \frac{1}{40} = 0.6 \] Converting \( 0.6 \) to a fraction: \[ 0.6 = \frac{6}{10} = \frac{3}{5} \] Now substitute: \[ x - \frac{1}{40} = \frac{3}{5} \] We need a common denominator to subtract: \[ \frac{3}{5} = \frac{24}{40} \] So: \[ x - \frac{1}{40} = \frac{24}{40} \] \[ x = \frac{24}{40} + \frac{1}{40} \] \[ x = \frac{25}{40} = \frac{5}{8} \]
Summary of the values for \( x \):
- \( x = 46 \)
- \( x = -\frac{5}{8} \)
- \( x = \frac{5}{8} \)
- \( x = -24 \)
- \( x = \frac{5}{8} \)
The values that correspond to each equation are:
- First equation: 46
- Second equation: -0.625 (which is -5/8)
- Third equation: 0.625 (which is 5/8)
- Fourth equation: -24
- Fifth equation: 0.625 (which is 5/8)
Conclusion:
The equation with a different value of \( x \) is:
- \( x - 78 = -32 \), since \( x = 46 \) is different from all the others which yield values around 0.625 and -24.
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