Let's solve each equation step by step.
For the equation \(-2x - 4 = 3x\):
\[ -2x - 4 = 3x \] To isolate \(x\), first add \(2x\) to both sides: \[ -4 = 3x + 2x \] \[ -4 = 5x \] Now, divide both sides by 5: \[ x = -\frac{4}{5} \]
For the equation \(-1 - 3x = 2x + 1\):
\[ -1 - 3x = 2x + 1 \] Add \(3x\) to both sides: \[ -1 = 2x + 3x + 1 \] \[ -1 = 5x + 1 \] Now, subtract 1 from both sides: \[ -1 - 1 = 5x \] \[ -2 = 5x \] Divide both sides by 5: \[ x = -\frac{2}{5} \]
For the equation \(10(x + 2) = -7\):
\[ 10(x + 2) = -7 \] Divide both sides by 10: \[ x + 2 = -\frac{7}{10} \] Now, subtract 2 from both sides. Remember that \(2\) is the same as \(\frac{20}{10}\): \[ x = -\frac{7}{10} - \frac{20}{10} \] \[ x = -\frac{27}{10} \]
Summary of Solutions:
- \(x = -\frac{4}{5}\)
- \(x = -\frac{2}{5}\)
- \(x = -\frac{27}{10}\)