1. The problem is to solve the inequality $$4x^2 - 5x - 6 > 0$$. 2. To solve quadratic inequalities, first find the roots of the corresponding quadratic equation $$4x^2 - 5x - 6 = 0$$. 3. Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=4$, $b=-5$, and $c=-6$. 4. Calculate the discriminant: $$\Delta = (-5)^2 - 4 \times 4 \times (-6) = 25 + 96 = 121$$. 5. Find the roots: $$x = \frac{5 \pm \sqrt{121}}{8} = \frac{5 \pm 11}{8}$$. 6. So the roots are $$x_1 = \frac{5 - 11}{8} = \frac{-6}{8} = -\frac{3}{4}$$ and $$x_2 = \frac{5 + 11}{8} = \frac{16}{8} = 2$$. 7. Since the parabola opens upwards ($a=4>0$), the quadratic is positive outside the roots and negative between them. 8. Therefore, the solution to $$4x^2 - 5x - 6 > 0$$ is $$x < -\frac{3}{4}$$ or $$x > 2$$. 1. The problem is to write down the inequality shown on the number line with an open circle at -3 and a solid circle at 1 with an arrow pointing right from 1. 2. An open circle at -3 means $$x \neq -3$$ and a solid circle at 1 with an arrow to the right means $$x \geq 1$$. 3. The inequality shown is $$x \geq 1$$. 1. The problem is to solve the inequality $$4y - 13 \leq y + 8$$. 2. Subtract $y$ from both sides: $$4y - y - 13 \leq 8$$ which simplifies to $$3y - 13 \leq 8$$. 3. Add 13 to both sides: $$3y \leq 21$$. 4. Divide both sides by 3: $$y \leq 7$$. Final answers: - For Question 3: $$x < -\frac{3}{4} \text{ or } x > 2$$. - For Question 4(a): $$x \geq 1$$. - For Question 4(b): $$y \leq 7$$.