Question

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

34x+5=−14
3
4
𝑥
+
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
−
0.35
𝑥
−
0.52
=
1.93

negative 0.35 x minus 0.52 equals 1.93

−17x−34=14
−
1
7
𝑥
−
3
4
=
1
4
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

Answer 1

which one is it

Answer 2

To determine which of the given equations has a solution different from the rest, we will solve each equation for \( x \).

1. **Equation 1:** \( 34x + 5 = -14 \)
\[
34x = -14 - 5 \\
34x = -19 \\
x = -\frac{19}{34}
\]

2. **Equation 2:** \( \frac{3}{4}x + 5 = -\frac{1}{4} \)
\[
\frac{3}{4}x = -\frac{1}{4} - 5 \\
\frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} \\
\frac{3}{4}x = -\frac{21}{4} \\
x = -\frac{21}{4} \times \frac{4}{3} = -7
\]

3. **Equation 3:** \( -0.35x - 0.52 = 1.93 \)
\[
-0.35x = 1.93 + 0.52 = 2.45 \\
x = -\frac{2.45}{0.35} \approx -7
\]

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

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

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

The solutions for Equations 2 and 3 are approximately equal (\(-7\)), but Equation 4 has a solution of \( 7 \), and Equation 5 has a solution of \( \frac{5}{4} \). However, the solution from Equation 4 (\( 7 \)) is particularly different from the others.

Thus, the equation that has a solution different from the rest is:
**−17x−34=14 or − \frac{1}{7} x − \frac{3}{4} = \frac{1}{4}** leading to \( x = 7 \).

Answer 3

The equation that has a solution different from the rest is:

**−\(\frac{1}{7}\)x − \(\frac{3}{4}\) = \(\frac{1}{4}\)**

This equation has a solution of \( x = 7 \), while the other equations have solutions that are negative or fractional:

1. \( 34x + 5 = -14 \): \( x = -\frac{19}{34} \)
2. \( \frac{3}{4}x + 5 = -\frac{1}{4} \): \( x = -7 \)
3. \( -0.35x - 0.52 = 1.93 \): \( x \approx -7 \)
4. \( 12x - 3 = 12 \): \( x = \frac{5}{4} \)

So, the distinct solution is from the fourth equation: **\( x = 7 \)**.