Question

Which of the following equations has a solution different from the rest? (1 point)
Responses

1/2x−3=1/2
Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction

−0.35x−0.52=1.93
negative 0.35 x minus 0.52 equals 1.93

−1/7x−3/4=1/4
negative Start Fraction 1 over 7 End Fraction x minus Start Fraction 3 over 4 End Fraction equals Start Fraction 1 over 4 End Fraction

3/4x+5=−1/4

Answers

Answered by GPT-4o mini
To determine which of the given equations has a solution different from the others, we will solve each equation one by one.

1. **Equation 1:**
\[
\frac{1}{2}x - 3 = \frac{1}{2}
\]
Adding 3 to both sides:
\[
\frac{1}{2}x = \frac{1}{2} + 3 \implies \frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2}
\]
Multiplying both sides by 2:
\[
x = 7
\]

2. **Equation 2:**
\[
-0.35x - 0.52 = 1.93
\]
Adding 0.52 to both sides:
\[
-0.35x = 1.93 + 0.52 \implies -0.35x = 2.45
\]
Dividing by -0.35:
\[
x = \frac{2.45}{-0.35} \approx -7
\]

3. **Equation 3:**
\[
-\frac{1}{7}x - \frac{3}{4} = \frac{1}{4}
\]
Adding \(\frac{3}{4}\) to both sides:
\[
-\frac{1}{7}x = \frac{1}{4} + \frac{3}{4} \implies -\frac{1}{7}x = 1
\]
Multiplying by -7:
\[
x = -7
\]

4. **Equation 4:**
\[
\frac{3}{4}x + 5 = -\frac{1}{4}
\]
Subtracting 5 from both sides:
\[
\frac{3}{4}x = -\frac{1}{4} - 5 \implies \frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} = -\frac{21}{4}
\]
Multiplying by \(\frac{4}{3}\):
\[
x = -\frac{21}{4} \cdot \frac{4}{3} = -\frac{21}{3} = -7
\]

Now, summarizing the solutions:
- Equation 1: \(x = 7\)
- Equation 2: \(x \approx -7\)
- Equation 3: \(x = -7\)
- Equation 4: \(x = -7\)

The only equation that has a solution different from the others is Equation 1, which has a solution of \(x = 7\), while the rest have solutions of \(x \approx -7\).

Thus, the answer is:
**1/2x−3=1/2**.
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