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 + 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 + 98 = 74

Answer 1

To determine which of the given equations has a different value of \(x\), we need to solve each equation for \(x\).

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

\[
x = 0.6 + 0.025 = 0.625
\]

2. **Equation 2:** \(x + 0.875 = 1.5\)

\[
x = 1.5 - 0.875 = 0.625
\]

3. **Equation 3:** \(x - 78 = -32\)

\[
x = -32 + 78 = 46
\]

4. **Equation 4:** \(x - \frac{7}{8} = -\frac{3}{2}\)

To solve this, first convert \(-\frac{3}{2}\) to have a common denominator:

\(-\frac{3}{2} = -\frac{12}{8}\)

Now, we can solve:

\[
x - \frac{7}{8} = -\frac{12}{8}
\]

\[
x = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8}
\]

5. **Equation 5:** \(x + 98 = 74\)

\[
x = 74 - 98 = -24
\]

Now we summarize the results for each equation:

1. \(x = 0.625\)
2. \(x = 0.625\)
3. \(x = 46\)
4. \(x = -\frac{5}{8} \text{ (or -0.625)}\)
5. \(x = -24\)

From these results, we can see that **Equation 3 (\(x - 78 = -32\))** has a different value of \(x\) (46) compared to all the others.

Thus, the answer is: **\(x - 78 = -32\)**.