2x-5 = -4x+7 4x+1 = x+4 6x−5 = 2x+7 −2x−7 = 3x+14 9x−3 = 5x+9 −3x+5 = -x-1 2x+5 = 4x−3 8x−2 = 6x+10

$$
2x + 4x - 5 = -4x + 4x + 7
$$
$$
6x - 5 = 7
$$

$$
6x - 5 + 5 = 7 + 5
$$
$$
6x = 12
$$

$$
\frac{6x}{6} = \frac{12}{6}
$$
$$
x = 2
$$
The solution is $\boxed{x = 2}$.

$$
4x - x + 1 = x - x + 4
$$
$$
3x + 1 = 4
$$

$$
3x + 1 - 1 = 4 - 1
$$
$$
3x = 3
$$

$$
\frac{3x}{3} = \frac{3}{3}
$$
$$
x = 1
$$
The solution is $\boxed{x = 1}$.

$$
6x - 2x - 5 = 2x - 2x + 1
$$
$$
4x - 5 = 1
$$

$$
4x - 5 + 5 = 1 + 5
$$
$$
4x = 6
$$

$$
\frac{4x}{4} = \frac{6}{4}
$$
$$
x = \frac{3}{2}
$$
The solution is $\boxed{x = \frac{3}{2}}$.

$$
-2x + 3x - 1 = -3x + 3x + 14
$$
$$
x - 1 = 14
$$

$$
x - 1 + 1 = 14 + 1
$$
$$
x = 15
$$
The solution is $\boxed{x = 15}$.

$$
9x - 5x - 3 = 5x - 5x + 9
$$
$$
4x - 3 = 9
$$

$$
4x - 3 + 3 = 9 + 3
$$
$$
4x = 12
$$

$$
\frac{4x}{4} = \frac{12}{4}
$$
$$
x = 3
$$
The solution is $\boxed{x = 3}$.

$$
-3x + x + 5 = -x + x - 1
$$
$$
-2x + 5 = -1
$$

$$
-2x + 5 - 5 = -1 - 5
$$
$$
-2x = -6
$$

$$
\frac{-2x}{-2} = \frac{-6}{-2}
$$
$$
x = 3
$$
The solution is $\boxed{x = 3}$.

$$
2x - 2x + 5 = 4x - 2x - 3
$$
$$
5 = 2x - 3
$$

$$
5 + 3 = 2x - 3 + 3
$$
$$
8 = 2x
$$

$$
\frac{8}{2} = \frac{2x}{2}
$$
$$
x = 4
$$
The solution is $\boxed{x = 4}$.

$$
x + 6x - 2 = -6x + 6x + 10
$$
$$
7x - 2 = 10
$$

$$
7x - 2 + 2 = 10 + 2
$$
$$
7x = 12
$$

$$
\frac{7x}{7} = \frac{12}{7}
$$
$$
x = \frac{12}{7}
$$
The solution is $\boxed{x = \frac{12}{7}}$.