1. **Solve the inequality**: $-3x < 12$ and find the minimum integral solution for $x$. - Start with the inequality: $-3x < 12$. - Divide both sides by $-3$. Remember, dividing by a negative number reverses the inequality sign. $$x > \frac{12}{-3}$$ $$x > -4$$ - So, $x$ must be greater than $-4$. - The minimum integral solution is the smallest integer greater than $-4$, which is $-3$. 2. **Factorize**: $x^2 - 9x - 36$ - We look for two numbers that multiply to $-36$ and add to $-9$. - These numbers are $-12$ and $3$ because $-12 \times 3 = -36$ and $-12 + 3 = -9$. - So, factorization is: $$(x - 12)(x + 3)$$ 3. **Solve the system of equations**: $$2a - 3b = -3$$ $$a + 3b = 12$$ - Add the two equations to eliminate $b$: $$(2a - 3b) + (a + 3b) = -3 + 12$$ $$3a = 9$$ $$a = 3$$ - Substitute $a=3$ into the second equation: $$3 + 3b = 12$$ $$3b = 9$$ $$b = 3$$ 4. **Simplify**: $$\frac{5}{5x + y} - \frac{2 - x}{5x + y}$$ - Since denominators are the same, combine the numerators: $$\frac{5 - (2 - x)}{5x + y} = \frac{5 - 2 + x}{5x + y} = \frac{3 + x}{5x + y}$$ **Final answers:** 1. Minimum integral solution for $x$ is $-3$. 2. Factorization: $(x - 12)(x + 3)$. 3. $a = 3$, $b = 3$. 4. Simplified expression: $\frac{3 + x}{5x + y}$.