Let's solve each equation step by step.
Solving the first equation:
\(-8x - 3 = -6x\)To isolate \(x\), first add \(8x\) to both sides:
\[ -3 = -6x + 8x \] \[ -3 = 2x \]
Now, divide by 2:
\[ x = -\frac{3}{2} \quad \text{or} \quad x = -1.5 \]
Solving the second equation:
\(-5 + 2x = -2x - 3\)First, add \(2x\) to both sides:
\[ -5 + 2x + 2x = -3 \] \[ -5 + 4x = -3 \]
Next, add 5 to both sides:
\[ 4x = -3 + 5 \] \[ 4x = 2 \]
Now, divide by 4:
\[ x = \frac{2}{4} \quad \text{or} \quad x = \frac{1}{2} \]
Solving the third equation:
\(4(x-6) = 5\)Start by distributing the 4:
\[ 4x - 24 = 5 \]
Then, add 24 to both sides:
\[ 4x = 5 + 24 \] \[ 4x = 29 \]
Finally, divide by 4:
\[ x = \frac{29}{4} \quad \text{or} \quad x = 7.25 \]
Summary of solutions:
- \(x = -\frac{3}{2}\) or \(x = -1.5\)
- \(x = \frac{1}{2}\)
- \(x = \frac{29}{4}\) or \(x = 7.25\)