To determine which equation has a solution different from the rest, let's solve each equation for \( x \):
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Equation 1: \[ -0.35x - 0.52 = 1.93 \] First, add \( 0.52 \) to both sides: \[ -0.35x = 1.93 + 0.52 \implies -0.35x = 2.45 \] Now, divide by \( -0.35 \): \[ x = \frac{2.45}{-0.35} \approx -7 \]
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Equation 2: \[ \frac{1}{2}x - 3 = \frac{1}{2} \] Add \( 3 \) to both sides: \[ \frac{1}{2}x = \frac{1}{2} + 3 \implies \frac{1}{2}x = \frac{1}{2} + \frac{6}{2} \implies \frac{1}{2}x = \frac{7}{2} \] Multiply both sides by \( 2 \): \[ x = 7 \]
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Equation 3: \[ -\frac{1}{7}x - \frac{3}{4} = \frac{1}{4} \] Add \( \frac{3}{4} \) to both sides: \[ -\frac{1}{7}x = \frac{1}{4} + \frac{3}{4} \implies -\frac{1}{7}x = 1 \] Multiply both sides by \( -7 \): \[ x = -7 \]
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Equation 4: \[ \frac{3}{4}x + 5 = -\frac{1}{4} \] Subtract \( 5 \) from both sides: \[ \frac{3}{4}x = -\frac{1}{4} - 5 \implies \frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} \implies \frac{3}{4}x = -\frac{21}{4} \] Multiply both sides by \( \frac{4}{3} \): \[ x = -7 \]
Now we have the solutions:
- Equation 1: \( x \approx -7 \)
- Equation 2: \( x = 7 \)
- Equation 3: \( x = -7 \)
- Equation 4: \( x = -7 \)
The equation that has a solution different from the rest is: Equation 2: \( \frac{1}{2}x - 3 = \frac{1}{2} \) with solution \( x = 7 \).