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Which of the following equations has a solution different from the rest? (1 point) Responses 3/4x+5=−1/4 Start Fraction 3 over 4 End Fraction x plus 5 equals negative Start Fraction 1 over 4 End Fraction −0.35x−0.52=1.93 negative 0.35 x minus 0.52 equals 1.93 1/2x−3=1/2 Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction −1/7x−3/4=1/4

1 answer

To determine which equation has a different solution from the rest, we can solve each equation one by one.

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

    \(\frac{3}{4}x = -\frac{1}{4} - 5\)

    \(\frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} = -\frac{21}{4}\)

    \(x = -\frac{21}{4} \cdot \frac{4}{3} = -\frac{21}{3} = -7\)

  2. Equation 2: \(-0.35x - 0.52 = 1.93\)

    \(-0.35x = 1.93 + 0.52\)

    \(-0.35x = 2.45\)

    \(x = \frac{2.45}{-0.35} \approx -7\)

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

    \(\frac{1}{2}x = \frac{1}{2} + 3\)

    \(\frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2}\)

    \(x = 7\)

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

    \(-\frac{1}{7}x = \frac{1}{4} + \frac{3}{4}\)

    \(-\frac{1}{7}x = 1\)

    \(x = -7\)

Now we have the solutions for each equation:

  • Equation 1: \(x = -7\)
  • Equation 2: \(x \approx -7\)
  • Equation 3: \(x = 7\)
  • Equation 4: \(x = -7\)

The equation that has a solution different from the rest is Equation 3, which has the solution \(x = 7\). The others yield \(x \approx -7\).