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

Question

Responses

−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

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

3/4x+5=−1/4

Answer 1

To determine which equation has a solution different from the rest, we can solve each equation for \( x \).

1. Equation: \(-\frac{1}{7}x - \frac{3}{4} = \frac{1}{4}\)

   To isolate \( x \): \[ -\frac{1}{7}x = \frac{1}{4} + \frac{3}{4} \] \[ -\frac{1}{7}x = 1 \] Multiply both sides by -7: \[ x = -7 \]

2. Equation: \(\frac{1}{2}x - 3 = \frac{1}{2}\)

   Rearranging: \[ \frac{1}{2}x = \frac{1}{2} + 3 \] \[ \frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2} \] Multiply both sides by 2: \[ x = 7 \]

3. Equation: \(-0.35x - 0.52 = 1.93\)

   Rearranging: \[ -0.35x = 1.93 + 0.52 \] \[ -0.35x = 2.45 \] Multiply both sides by -1/0.35: \[ x = -\frac{2.45}{0.35} \approx -7 \]

4. Equation: \(\frac{3}{4}x + 5 = -\frac{1}{4}\)

   Rearranging: \[ \frac{3}{4}x = -\frac{1}{4} - 5 \] \[ \frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} = -\frac{21}{4} \] Multiply both sides by \(\frac{4}{3}\): \[ x = -\frac{21}{3} = -7 \]

Summary of solutions:

• First equation: \( x = -7 \)
• Second equation: \( x = 7 \)
• Third equation: \( x \approx -7 \)
• Fourth equation: \( x = -7 \)

The second equation is the only one with a solution different from the others, which is \( x = 7 \).