1. State the problem: Find the solution set for the equation $2x - 5 = 9$. 2. Use the formula: To solve for $x$, isolate $x$ by performing inverse operations. 3. Add 5 to both sides: $$2x - 5 + 5 = 9 + 5$$ which simplifies to $$2x = 14$$. 4. Divide both sides by 2: $$\frac{2x}{2} = \frac{14}{2}$$ which simplifies to $$x = 7$$. 5. The solution set is $\{7\}$. --- 1. State the problem: Find the solution set for the inequality $3x + 4 > 10$. 2. Use the formula: To solve inequalities, isolate $x$ and remember to reverse the inequality sign when multiplying or dividing by a negative number. 3. Subtract 4 from both sides: $$3x + 4 - 4 > 10 - 4$$ which simplifies to $$3x > 6$$. 4. Divide both sides by 3: $$\frac{3x}{3} > \frac{6}{3}$$ which simplifies to $$x > 2$$. 5. The solution set is $\{x | x > 2\}$. --- 1. State the problem: Find the solution set for the quadratic equation $x^2 - 4x - 5 = 0$. 2. Use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=-4$, and $c=-5$. 3. Calculate the discriminant: $$b^2 - 4ac = (-4)^2 - 4(1)(-5) = 16 + 20 = 36$$. 4. Calculate the roots: $$x = \frac{-(-4) \pm \sqrt{36}}{2(1)} = \frac{4 \pm 6}{2}$$. 5. Find the two solutions: $$x = \frac{4 + 6}{2} = 5$$ and $$x = \frac{4 - 6}{2} = -1$$. 6. The solution set is $\{-1, 5\}$.