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 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 find which equation has a solution different from the rest, let's solve each equation one by one.

1. **Equation 1:**
\(-17x - 34 = 14\)

Adding \(34\) to both sides:
\(-17x = 14 + 34\)
\(-17x = 48\)

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

Multiplying both sides by \(7\):
\(x = 7\)

3. **Equation 3:**
\(12x - 3 = 12\)

Adding \(3\) to both sides:
\(12x = 12 + 3\)
\(12x = 15\)

Dividing by \(12\):
\(x = \frac{15}{12} = \frac{5}{4}\)

4. **Equation 4:**
\(\frac{1}{2}x - 3 = \frac{1}{2}\)

Adding \(3\) to both sides:
\(\frac{1}{2}x = \frac{1}{2} + 3\)
\(\frac{1}{2}x = \frac{1}{2} + \frac{6}{2} = \frac{7}{2}\)

Multiplying by \(2\):
\(x = 7\)

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

Subtracting \(5\) from both sides:
\(34x = -14 - 5\)
\(34x = -19\)

Dividing by \(34\):
\(x = -\frac{19}{34}\)

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

Adding \(0.52\) to both sides:
\(-0.35x = 1.93 + 0.52\)
\(-0.35x = 2.45\)

Dividing by \(-0.35\):
\(x = \frac{-2.45}{0.35} = -7\)

Now let's summarize the solutions:
- Equation 1: \(x = -\frac{48}{17}\)
- Equation 2: \(x = 7\)
- Equation 3: \(x = \frac{5}{4}\)
- Equation 4: \(x = 7\)
- Equation 5: \(x = -\frac{19}{34}\)
- Equation 6: \(x = -7\)

The solutions for Equations 2 and 4 are both \(x = 7\). Hence, they are the same.

Other solutions are:
- \(-\frac{48}{17} \approx -2.82\)
- \(\frac{5}{4} = 1.25\)
- \(-\frac{19}{34} \approx -0.56\)
- \(-7\)

The solution that stands out is **\(x = 7\)** for both 2 and 4 while all others are different. Therefore, the unique equation in terms of solution is **Equation 3: \(x = \frac{5}{4}\)** which has a different solution than the rest.

Thus, **the equation with a solution different from the rest is Equation 3: \(12x - 3 = 12\)**.