We are asked to solve the following equations: 4. $\frac{3}{4}y + 2y = \frac{1}{2} + 4y - 3$ 6. $0.3(6+x) = 0.4(8-x)$ 8. $\frac{2}{5x} - \frac{5}{2x} = \frac{1}{10}$ 10. $\frac{3-5x}{7} - \frac{x}{4} = \frac{1}{2} + \frac{5-4x}{8}$ 11. $\frac{3(x-1)}{4} - 2 = 5x - \frac{x-2}{2}$ Let's solve each equation.

1. Problem Description

We are asked to solve the following equations:

4. $\frac{3}{4}y + 2y = \frac{1}{2} + 4y - 3$

6. $0.3(6+x) = 0.4(8-x)$

8. $\frac{2}{5x} - \frac{5}{2x} = \frac{1}{10}$

1

0. $\frac{3-5x}{7} - \frac{x}{4} = \frac{1}{2} + \frac{5-4x}{8}$

1

1. $\frac{3(x-1)}{4} - 2 = 5x - \frac{x-2}{2}$

Let's solve each equation.

2. Solution Steps

4. $\frac{3}{4}y + 2y = \frac{1}{2} + 4y - 3$

$\frac{3}{4}y + \frac{8}{4}y = 4y - \frac{5}{2}$

$\frac{11}{4}y = 4y - \frac{5}{2}$

$\frac{11}{4}y - \frac{16}{4}y = -\frac{5}{2}$

$-\frac{5}{4}y = -\frac{5}{2}$

$y = -\frac{5}{2} \cdot (-\frac{4}{5})$

$y = 2$

6. $0.3(6+x) = 0.4(8-x)$

$1.8 + 0.3x = 3.2 - 0.4x$

$0.3x + 0.4x = 3.2 - 1.8$

$0.7x = 1.4$

$x = \frac{1.4}{0.7}$

$x = 2$

8. $\frac{2}{5x} - \frac{5}{2x} = \frac{1}{10}$

$\frac{4}{10x} - \frac{25}{10x} = \frac{1}{10}$

$\frac{4-25}{10x} = \frac{1}{10}$

$\frac{-21}{10x} = \frac{1}{10}$

$-210 = 10x$

$x = -21$

9. $\frac{3-5x}{7} - \frac{x}{4} = \frac{1}{2} + \frac{5-4x}{8}$

Multiply by 56:

$8(3-5x) - 14x = 28 + 7(5-4x)$

$24 - 40x - 14x = 28 + 35 - 28x$

$24 - 54x = 63 - 28x$

$-54x + 28x = 63 - 24$

$-26x = 39$

$x = \frac{39}{-26}$

$x = -\frac{3}{2}$

1

0. $\frac{3(x-1)}{4} - 2 = 5x - \frac{x-2}{2}$

Multiply by 4:

$3(x-1) - 8 = 20x - 2(x-2)$

$3x - 3 - 8 = 20x - 2x + 4$

$3x - 11 = 18x + 4$

$3x - 18x = 4 + 11$

$-15x = 15$

$x = -1$

3. Final Answer

4. $y = 2$

5. $x = 2$

6. $x = -21$

7. $x = -\frac{3}{2}$

8. $x = -1$