Which of the following equations has a different value of x

Question

than the others?(1 point)
Responses

x − 78 = −32
x minus Start Fraction 7 over 8 End Fraction equals negative Start Fraction 3 over 2 End Fraction

x + 0.875 = 1.5
x plus 0.875 equals 1.5

x + 98 = 74
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
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Answer 1

Let's solve each equation to determine the value of \( x \) for each, and find which one has a different value.

1. Equation 1: \( x - 78 = -32 \)

   \[ x = -32 + 78 = 46 \]

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

   To solve for \( x \):

   \[ x = -\frac{3}{2} + \frac{7}{8} \] Converting \(-\frac{3}{2}\) to have a denominator of 8: \(-\frac{3}{2} = -\frac{12}{8}\)

   \[ x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \]

3. Equation 3: \( x + 0.875 = 1.5 \)

   \[ x = 1.5 - 0.875 = 0.625 \]

4. Equation 4: \( x + 98 = 74 \)

   \[ x = 74 - 98 = -24 \]

5. Equation 5: \( x - 0.025 = 0.6 \)

   \[ x = 0.6 + 0.025 = 0.625 \]

Now we have the values of \( x \) for each equation:

1. \( x = 46 \)
2. \( x = -\frac{5}{8} \) (or -0.625)
3. \( x = 0.625 \)
4. \( x = -24 \)
5. \( x = 0.625 \)

Among these values, \( 46 \), \( -\frac{5}{8} \), and \( -24 \) are different from the others, but \( x = 0.625 \) appears twice.

Thus, the equation that has a different value of \( x \) than the others is:

Equation 1: \( x - 78 = -32 \) with \( x = 46 \).