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Question

Which of the following equations has a different value of x
than the others?(1 point)
Responses

x + 0.875 = 1.5
x plus 0.875 equals 1.5

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

x − 0.025 = 0.6
x minus 0.025 equals 0.6

x + 9/8 = 7/4

1 answer

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

  1. Equation 1: \[ x + 0.875 = 1.5 \] Subtracting 0.875 from both sides: \[ x = 1.5 - 0.875 = 0.625 \]

  2. Equation 2: \[ x - \frac{7}{8} = -\frac{3}{2} \] Adding \(\frac{7}{8}\) to both sides: \[ x = -\frac{3}{2} + \frac{7}{8} \] To combine these, convert \(-\frac{3}{2}\) to eighths: \[ -\frac{3}{2} = -\frac{12}{8} \] Now combine: \[ x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \]

  3. Equation 3: \[ x - 0.025 = 0.6 \] Adding 0.025 to both sides: \[ x = 0.6 + 0.025 = 0.625 \]

  4. Equation 4: \[ x + \frac{9}{8} = \frac{7}{4} \] Subtracting \(\frac{9}{8}\) from both sides: \[ x = \frac{7}{4} - \frac{9}{8} \] Convert \(\frac{7}{4}\) to eighths: \[ \frac{7}{4} = \frac{14}{8} \] Now combine: \[ x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \]

Now we have the resulting values for \( x \):

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

The only equation that results in a different value of \( x \) is the second equation:

Response: \( x - \frac{7}{8} = -\frac{3}{2} \) (which gives \( x = -\frac{5}{8} \)).