Let's solve each equation step by step to verify or find the correct values of \(x\).
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For the equation: \[ -10 - 2x = -8 \] Add 10 to both sides: \[ -2x = -8 + 10 \ -2x = 2 \] Divide by -2: \[ x = -1 \] Correct: \(x = -1\)
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For the equation: \[ 5 = 2x - 11 \] Add 11 to both sides: \[ 5 + 11 = 2x \ 16 = 2x \] Divide by 2: \[ x = 8 \] Correct: \(x = 8\)
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For the equation: \[ \frac{11}{4}x + 9 = 31 \] Subtract 9 from both sides: \[ \frac{11}{4}x = 31 - 9 \ \frac{11}{4}x = 22 \] Multiply both sides by \(\frac{4}{11}\): \[ x = 22 \cdot \frac{4}{11} \ x = 8 \] Correct: \(x = 8\)
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For the equation: \[ \frac{3}{7}x - 4 = -1 \] Add 4 to both sides: \[ \frac{3}{7}x = -1 + 4 \ \frac{3}{7}x = 3 \] Multiply both sides by \(\frac{7}{3}\): \[ x = 3 \cdot \frac{7}{3} \ x = 7 \] Correct: \(x = 7\)
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For the equation: \[ 3 - \frac{6}{5}x = -3 \] Subtract 3 from both sides: \[ -\frac{6}{5}x = -3 - 3 \ -\frac{6}{5}x = -6 \] Multiply both sides by \(-\frac{5}{6}\): \[ x = -6 \cdot -\frac{5}{6} \ x = 5 \] Correct: \(x = 5\)
All the given solutions for \(x\) are correct:
- \(x = -1\)
- \(x = 8\)
- \(x = 8\)
- \(x = 7\)
- \(x = 5\)