Which of the following equations has a different value of x

Question

than the others?(1 point)
Responses

x + 9/8 = 7/4
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

x + 0.875 = 1.5
x plus 0.875 equals 1.5

x − 7/8 = −3/2

Answer 1

Let's solve each equation for \( x \):

1. For the equation \( x + \frac{9}{8} = \frac{7}{4} \): \[ x = \frac{7}{4} - \frac{9}{8} \] First, convert \( \frac{7}{4} \) to have a common denominator of 8: \[ \frac{7}{4} = \frac{14}{8} \] Now, \[ x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \]

2. For the equation \( x - 0.025 = 0.6 \): \[ x = 0.6 + 0.025 = 0.625 \]

3. For the equation \( x + 0.875 = 1.5 \): \[ x = 1.5 - 0.875 \] Convert \( 1.5 \) to a fraction: \[ 1.5 = \frac{3}{2} = \frac{6}{4} = \frac{12}{8} \] Now, \[ x = \frac{12}{8} - \frac{7}{8} = \frac{5}{8} \]

4. For the equation \( x - \frac{7}{8} = -\frac{3}{2} \): \[ x = -\frac{3}{2} + \frac{7}{8} \] Convert \( -\frac{3}{2} \) to have a common denominator of 8: \[ -\frac{3}{2} = -\frac{12}{8} \] So, \[ x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \]

Now we summarize the values of \( x \):

• \( x + \frac{9}{8} = \frac{7}{4} \) gives \( x = \frac{5}{8} \)
• \( x - 0.025 = 0.6 \) gives \( x = 0.625 \) (which is \( \frac{5}{8} \))
• \( x + 0.875 = 1.5 \) gives \( x = \frac{5}{8} \)
• \( x - \frac{7}{8} = -\frac{3}{2} \) gives \( x = -\frac{5}{8} \)

From the computations:

• The first three equations give \( x = \frac{5}{8} \)
• The last equation gives \( x = -\frac{5}{8} \)

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

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