1. The problem asks to solve for the values of $x$ in the equations given in parts 3 and 4 of the picture. 2. For part 3, the equation is $\frac{2x+3}{x-1} = 4$. 3. To solve this, multiply both sides by $x-1$ to eliminate the denominator: $$\cancel{(x-1)} \cdot \frac{2x+3}{\cancel{x-1}} = 4 \cdot (x-1)$$ which simplifies to $$2x + 3 = 4x - 4$$ 4. Rearrange terms to isolate $x$: $$2x + 3 = 4x - 4$$ $$3 + 4 = 4x - 2x$$ $$7 = 2x$$ 5. Divide both sides by 2: $$\frac{7}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ which gives $$x = \frac{7}{2}$$ 6. For part 4, the equation is $\frac{3x-1}{2} + \frac{x+5}{3} = 4$. 7. Find a common denominator for the fractions, which is 6, and multiply both sides by 6: $$6 \cdot \left( \frac{3x-1}{2} + \frac{x+5}{3} \right) = 6 \cdot 4$$ 8. Distribute 6: $$3(3x - 1) + 2(x + 5) = 24$$ 9. Expand the terms: $$9x - 3 + 2x + 10 = 24$$ 10. Combine like terms: $$11x + 7 = 24$$ 11. Subtract 7 from both sides: $$11x = 24 - 7$$ $$11x = 17$$ 12. Divide both sides by 11: $$\frac{17}{\cancel{11}} = \frac{11x}{\cancel{11}}$$ which gives $$x = \frac{17}{11}$$ Final answers: - For part 3: $x = \frac{7}{2}$ - For part 4: $x = \frac{17}{11}$