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

Question

Responses

x − 0.025 = 0.6
x minus 0.025 equals 0.6

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 + 9/8 = 7/4

Answer 1

To determine which equation has a different value for \( x \), we'll solve each equation individually:

1. Equation 1: \[ x - 0.025 = 0.6 \] Adding \( 0.025 \) to both sides: \[ x = 0.6 + 0.025 = 0.625 \]

2. Equation 2: \[ x + 0.875 = 1.5 \] Subtracting \( 0.875 \) from both sides: \[ x = 1.5 - 0.875 = 0.625 \]

3. Equation 3: \[ x - \frac{7}{8} = -\frac{3}{2} \] Adding \( \frac{7}{8} \) to both sides: \[ x = -\frac{3}{2} + \frac{7}{8} \] To perform this addition, we need a common denominator. The common denominator of 2 and 8 is 8: \[ -\frac{3}{2} = -\frac{12}{8} \] Now we can add: \[ x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \]

4. Equation 4: \[ x + \frac{9}{8} = \frac{7}{4} \] Subtracting \( \frac{9}{8} \) from both sides: \[ x = \frac{7}{4} - \frac{9}{8} \] Again, we need a common denominator. The common denominator of 4 and 8 is 8: \[ \frac{7}{4} = \frac{14}{8} \] So we have: \[ x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \]

Summary of values for \( x \):

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

The equation that has a different value of \( x \) is Equation 3: \( x - \frac{7}{8} = -\frac{3}{2} \) (which yields \( x = -\frac{5}{8} \)).