1. Consider the expression: $$3(x - 2) - 4(x + 5)$$. 2. The problem is to simplify this expression by removing the brackets and combining like terms. 3. First, distribute the 3 across the terms inside the first bracket: $$3 \times x = 3x$$ and $$3 \times (-2) = -6$$, so $$3(x - 2) = 3x - 6$$. 4. Next, distribute the -4 across the terms inside the second bracket: $$-4 \times x = -4x$$ and $$-4 \times 5 = -20$$, so $$-4(x + 5) = -4x - 20$$. 5. Now substitute back into the expression: $$3x - 6 - 4x - 20$$. 6. Combine like terms: $$3x - 4x = -x$$ and $$-6 - 20 = -26$$. 7. So the simplified expression is $$-x - 26$$. This completes the step-by-step simplification showing bracket distribution and combining like terms carefully respecting signs.