Find All Complex Solutions 8+2x-1=x-2-5x

$8 + 2 x - 1 = x - 2 - 5 x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x - 2 - 5 x = 8 + 2 x - 1$

Step 2

Subtract $5 x$ from $x$ .

$- 4 x - 2 = 8 + 2 x - 1$

Step 3

Subtract $1$ from $8$ .

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

Step 4

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$- 4 x - 2 - 2 x = 7$

Subtract $2 x$ from $- 4 x$ .

$- 6 x - 2 = 7$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$- 6 x = 7 + 2$

Add $7$ and $2$ .

$- 6 x = 9$

Step 6

Divide each term in $- 6 x = 9$ by $- 6$ and simplify.

Divide each term in $- 6 x = 9$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{9}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{9}{- 6}$

Divide $x$ by $1$ .

$x = \frac{9}{- 6}$

Simplify the right side.

Cancel the common factor of $9$ and $- 6$ .

Factor $3$ out of $9$ .

$x = \frac{3 (3)}{- 6}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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