Question

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

x − 0.025 = 0.6
x minus 0.025 equals 0.6

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
x plus Start Fraction 9 over 8 End Fraction equals Start Fraction 7 over 4 End Fraction

x + 0.875 = 1.5

Answer 1

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

1. **Equation 1:**
\( x - 0.025 = 0.6 \)
\( x = 0.6 + 0.025 = 0.625 \)

2. **Equation 2:**
\( x - \frac{7}{8} = -\frac{3}{2} \)
First, convert \(-\frac{3}{2}\) to eighths:
\(-\frac{3}{2} = -\frac{12}{8}\)
So, \( x - \frac{7}{8} = -\frac{12}{8} \)
\( x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \)

3. **Equation 3:**
\( x + \frac{9}{8} = \frac{7}{4} \)
First, convert \(\frac{7}{4}\) to eighths:
\(\frac{7}{4} = \frac{14}{8}\)
So, \( x + \frac{9}{8} = \frac{14}{8} \)
\( x = \frac{14}{8} - \frac{9}{8} = \frac{5}{8} \)

4. **Equation 4:**
\( x + 0.875 = 1.5 \)
Since \( 0.875 = \frac{7}{8} \) and \( 1.5 = \frac{3}{2} \):
\( x + \frac{7}{8} = \frac{3}{2} = \frac{12}{8} \)
\( x = \frac{12}{8} - \frac{7}{8} = \frac{5}{8} \)

Now, summarizing the values of \( x \):
1. From Equation 1: \( x = 0.625 \)
2. From Equation 2: \( x = -\frac{5}{8} \)
3. From Equation 3: \( x = \frac{5}{8} \)
4. From Equation 4: \( x = \frac{5}{8} \)

The values are:
- Equation 1: \( 0.625 \)
- Equation 2: \( -0.625 \) (which is \( -\frac{5}{8} \))
- Equation 3: \( 0.625 \) (which is \( \frac{5}{8} \))
- Equation 4: \( 0.625 \) (which is \( \frac{5}{8} \))

Since equation 2 gives a different value of \( x \), it is the equation with a different solution.

**Answer:** \( x - \frac{7}{8} = -\frac{3}{2} \)