Solve for x 5x-9-2=-5(2-x)-1

$5 x - 9 - 2 = - 5 (2 - x) - 1$

Step 1

Subtract $2$ from $- 9$ .

$5 x - 11 = - 5 (2 - x) - 1$

Step 2

Simplify $- 5 (2 - x) - 1$ .

Simplify each term.

Apply the distributive property.

$5 x - 11 = - 5 \cdot 2 - 5 (- x) - 1$

Multiply $- 5$ by $2$ .

$5 x - 11 = - 10 - 5 (- x) - 1$

Multiply $- 1$ by $- 5$ .

$5 x - 11 = - 10 + 5 x - 1$

Subtract $1$ from $- 10$ .

$5 x - 11 = 5 x - 11$

Step 3

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

Subtract $5 x$ from both sides of the equation.

$5 x - 11 - 5 x = - 11$

Combine the opposite terms in $5 x - 11 - 5 x$ .

Subtract $5 x$ from $5 x$ .

$0 - 11 = - 11$

Subtract $11$ from $0$ .

$- 11 = - 11$

Step 4

Since $- 11 = - 11$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$