Question

Question

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

12x−3=12
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

34x+5=−14

Answer 1

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

1. Equation: -17x - 34 = 14 \[ -17x = 14 + 34 \] \[ -17x = 48 \] \[ x = -\frac{48}{17} \approx -2.82 \]

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

3. Equation: \( 12x - 3 = 12 \) \[ 12x = 12 + 3 \] \[ 12x = 15 \] \[ x = \frac{15}{12} = \frac{5}{4} = 1.25 \]

4. Equation: \( \frac{1}{2}x - 3 = \frac{1}{2} \) \[ \frac{1}{2}x = \frac{1}{2} + 3 \] \[ \frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2} \] \[ x = 7 \]

5. Equation: -0.35x - 0.52 = 1.93 \[ -0.35x = 1.93 + 0.52 \] \[ -0.35x = 2.45 \] \[ x = -\frac{2.45}{0.35} \approx -7 \]

6. Equation: 34x + 5 = -14 \[ 34x = -14 - 5 \] \[ 34x = -19 \] \[ x = -\frac{19}{34} \approx -0.56 \]

Now, we summarize the solutions:

• 1: \( x \approx -2.82 \)
• 2: \( x = -7 \)
• 3: \( x = 1.25 \)
• 4: \( x = 7 \)
• 5: \( x \approx -7 \)
• 6: \( x \approx -0.56 \)

The solutions for equations 2 and 5 are both -7, but their other values are all different from each other.

Thus, the equation that has a solution different from the rest is:

Equation 3: \( 12x - 3 = 12 \) which leads to \( x = 1.25 \).