We need to solve four algebraic equations for $x$. The equations are: 9. $4x = x - (x - 2)$ 10. $7x = 3x - (x + 20)$ 11. $5x - 3(x - 1) = 39$ 12. $3x + 2(x - 5) = 15$

1. Problem Description

We need to solve four algebraic equations for $x$. The equations are:

9. $4x = x - (x - 2)$

1

0. $7x = 3x - (x + 20)$

1

1. $5x - 3(x - 1) = 39$

1

2. $3x + 2(x - 5) = 15$

2. Solution Steps

Solving equation 9:

$4x = x - (x - 2)$

$4x = x - x + 2$

$4x = 2$

$x = \frac{2}{4}$

$x = \frac{1}{2}$

Solving equation 10:

$7x = 3x - (x + 20)$

$7x = 3x - x - 20$

$7x = 2x - 20$

$7x - 2x = -20$

$5x = -20$

$x = \frac{-20}{5}$

$x = -4$

Solving equation 11:

$5x - 3(x - 1) = 39$

$5x - 3x + 3 = 39$

$2x + 3 = 39$

$2x = 39 - 3$

$2x = 36$

$x = \frac{36}{2}$

$x = 18$

Solving equation 12:

$3x + 2(x - 5) = 15$

$3x + 2x - 10 = 15$

$5x - 10 = 15$

$5x = 15 + 10$

$5x = 25$

$x = \frac{25}{5}$

$x = 5$

3. Final Answer

The solutions are:

9. $x = \frac{1}{2}$

1

0. $x = -4$

1

1. $x = 18$

1

2. $x = 5$