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

Question

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

34x+5=−14
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

Answer 1

To determine which equation has a solution different from the rest, we need to 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: \( \frac{1}{2}x - 3 = \frac{1}{2} \)

   \[ \frac{1}{2}x = \frac{1}{2} + 3 \ \frac{1}{2}x = \frac{1}{2} + \frac{6}{2} \ \frac{1}{2}x = \frac{7}{2} \ x = 7 \]

5. Equation: \( 34x + 5 = -14 \)

   \[ 34x = -14 - 5 \ 34x = -19 \ x = -\frac{19}{34} \approx -0.56 \]

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

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

Now, summarizing the solutions:

• First equation: \( x \approx -2.82 \)
• Second equation: \( x = -7 \)
• Third equation: \( x = 1.25 \)
• Fourth equation: \( x = 7 \)
• Fifth equation: \( x \approx -0.56 \)
• Sixth equation: \( x = -7 \)

The unique solutions are:

• \( -2.82 \)
• \( -7 \) (for both second and sixth equations)
• \( 1.25 \)
• \( 7 \)
• \( -0.56 \)

The equation with the solution that is different from all the rest is: \(12x - 3 = 12\) with solution \(x = 1.25\).