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

Responses

−17x−34=14
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

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

12x−3=12
Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction

34x+5=−14

1 answer

To determine which equation has a solution different from the rest, we'll solve each equation.

  1. Equation 1:
    \(-17x - 34 = 14\)
    Adding 34 to both sides:
    \(-17x = 48\)
    Dividing by -17:
    \(x = -\frac{48}{17}\)

  2. Equation 2:
    \(-\frac{1}{7}x - \frac{3}{4} = \frac{1}{4}\)
    Adding \(\frac{3}{4}\) to both sides:
    \(-\frac{1}{7}x = 1\)
    Multiplying both sides by -7:
    \(x = -7\)

  3. Equation 3:
    \(-0.35x - 0.52 = 1.93\)
    Adding 0.52 to both sides:
    \(-0.35x = 2.45\)
    Dividing by -0.35:
    \(x = -7\) (approximately, as \(-\frac{2.45}{0.35} = -7\))

  4. Equation 4:
    \(12x - 3 = 12\)
    Adding 3 to both sides:
    \(12x = 15\)
    Dividing by 12:
    \(x = \frac{15}{12} = \frac{5}{4}\)

  5. Equation 5:
    \(34x + 5 = -14\)
    Subtracting 5 from both sides:
    \(34x = -19\)
    Dividing by 34:
    \(x = -\frac{19}{34}\)

Now summarizing the solutions:

  1. \(x = -\frac{48}{17} \approx -2.82\)
  2. \(x = -7\)
  3. \(x = -7\)
  4. \(x = \frac{5}{4} = 1.25\)
  5. \(x = -\frac{19}{34} \approx -0.56\)

The unique and different solution is from Equation 4: \(x = \frac{5}{4}\).

Therefore, the equation that has a solution different from the rest is: 12x−3=12.