1. **Expand and simplify** the expression $(x + 5)(x + 4)(x - 3)$ to find constants $A$, $B$, $C$, and $D$. Start by expanding two brackets first: $$(x + 5)(x + 4) = x^2 + 4x + 5x + 20 = x^2 + 9x + 20$$ Now multiply this result by $(x - 3)$: $$ (x^2 + 9x + 20)(x - 3) = x^2(x - 3) + 9x(x - 3) + 20(x - 3) $$ $$ = x^3 - 3x^2 + 9x^2 - 27x + 20x - 60 $$ Combine like terms: $$ x^3 + ( -3x^2 + 9x^2 ) + ( -27x + 20x ) - 60 = x^3 + 6x^2 - 7x - 60 $$ So, $$ A = 1, B = 6, C = -7, D = -60 $$ 2. **Solve the simultaneous equations:** $$ 2x - 8y = -10 $$ $$ -10x - ? = ? $$ The second equation is incomplete in the prompt. Assuming it is $-10x - y = ?$, please provide the full second equation to solve. 3. **Solve the linear inequality:** $$ 2x + 10 \geq -10x - 7 $$ Add $10x$ to both sides: $$ 2x + 10x + 10 \geq -7 $$ $$ 12x + 10 \geq -7 $$ Subtract 10 from both sides: $$ 12x \geq -17 $$ Divide both sides by 12: $$ x \geq \frac{-17}{12} $$ This is the solution in lowest terms. **Final answers:** - For expansion: $A=1$, $B=6$, $C=-7$, $D=-60$ - For inequality: $x \geq \frac{-17}{12}$ Please provide the full second equation for question 7 to solve it completely.