To determine which equation has a solution different from the rest, I'll solve each equation one by one.
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Equation 1: \[ 34x + 5 = -14 \] Subtract 5 from both sides: \[ 34x = -14 - 5 \ 34x = -19 \ x = -\frac{19}{34} \]
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Equation 2: \[ \frac{3}{4} x + 5 = -\frac{1}{4} \] Subtract 5 from both sides: \[ \frac{3}{4} x = -\frac{1}{4} - 5 \ \frac{3}{4} x = -\frac{1}{4} - \frac{20}{4} \ \frac{3}{4} x = -\frac{21}{4} \] Multiply both sides by \(\frac{4}{3}\): \[ x = -7 \]
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Equation 3: \[ 12x - 3 = \frac{1}{2} x - 3 \] Add 3 to both sides: \[ 12x = \frac{1}{2} x \] Rearranging: \[ 12x - \frac{1}{2} x = 0 \ \left(12 - \frac{1}{2}\right)x = 0 \ \frac{24}{2}x - \frac{1}{2}x = 0 \ \frac{23}{2} x = 0 \ x = 0 \]
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Equation 4: \[ -0.35x - 0.52 = 1.93 \] Add 0.52 to both sides: \[ -0.35x = 1.93 + 0.52 \ -0.35x = 2.45 \] Divide by -0.35: \[ x = -\frac{2.45}{0.35} = -7 \]
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Equation 5: \[ -17x - 34 = 14 \] Add 34 to both sides: \[ -17x = 14 + 34 \ -17x = 48 \ x = -\frac{48}{17} \]
Now, let's summarize the solutions for each equation:
- \( x = -\frac{19}{34} \)
- \( x = -7 \)
- \( x = 0 \)
- \( x = -7 \)
- \( x = -\frac{48}{17} \)
The only equation with a different solution is Equation 3, which has a solution of \( x = 0 \).
Final Answer: Equation 3 has a solution different from the rest.
1 answer