Question

One- & Two-Step Equations Unit Test
2 of 152 of 15 Items
Question
Which of the following equations has a different value of x
than the others?(1 point)
Responses

x + 98 = 74
x plus Start Fraction 9 over 8 End Fraction equals Start Fraction 7 over 4 End Fraction

x + 0.875 = 1.5
x plus 0.875 equals 1.5

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

x − 0.025 = 0.6

Answer 1

To determine which equation gives a different value of \( x \), we'll solve each equation one by one.

1. **Equation: \( x + 98 = 74 \)**
\[
x = 74 - 98 \\
x = -24
\]

2. **Equation: \( x + \frac{9}{8} = \frac{7}{4} \)**
Convert \( \frac{7}{4} \) to have a common denominator with \( \frac{9}{8} \):
\[
\frac{7}{4} = \frac{14}{8} \\
x + \frac{9}{8} = \frac{14}{8} \\
x = \frac{14}{8} - \frac{9}{8} \\
x = \frac{5}{8}
\]

3. **Equation: \( x + 0.875 = 1.5 \)**
\[
x = 1.5 - 0.875 \\
x = 0.625
\]

4. **Equation: \( x - 78 = -32 \)**
\[
x = -32 + 78 \\
x = 46
\]

5. **Equation: \( x - 0.025 = 0.6 \)**
\[
x = 0.6 + 0.025 \\
x = 0.625
\]

Now, let's summarize the values of \( x \) from each equation:
- From the first equation: \( x = -24 \)
- From the second equation: \( x = \frac{5}{8} = 0.625 \)
- From the third equation: \( x = 0.625 \)
- From the fourth equation: \( x = 46 \)
- From the fifth equation: \( x = 0.625 \)

The values of \( x \) are:
- \( -24 \)
- \( 0.625 \) (occurs in multiple equations)
- \( 46 \)

The equations that provide different values for \( x \) compared to the others are:
- **\( x + 98 = 74 \)** (gives \( -24 \))
- **\( x - 78 = -32 \)** (gives \( 46 \))

Both \( -24 \) and \( 46 \) are different from \( 0.625 \). However, since the question asks for the one that differs from the rest, we can see that:

The equation \( x + 98 = 74 \) yields \( x = -24 \) which is quite distinct from the others.

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

**\( x + 98 = 74 \)**.