Solve for x -(-x+1)=x-1

$- (- x + 1) = x - 1$

Step 1

Simplify $- (- x + 1)$ .

Rewrite.

$0 + 0 - (- x + 1) = x - 1$

Simplify by adding zeros.

$- (- x + 1) = x - 1$

Apply the distributive property.

$- - x - 1 \cdot 1 = x - 1$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$1 x - 1 \cdot 1 = x - 1$

Multiply $x$ by $1$ .

$x - 1 \cdot 1 = x - 1$

Multiply $- 1$ by $1$ .

$x - 1 = x - 1$

Step 2

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

Subtract $x$ from both sides of the equation.

$x - 1 - x = - 1$

Combine the opposite terms in $x - 1 - x$ .

Subtract $x$ from $x$ .

$0 - 1 = - 1$

Subtract $1$ from $0$ .

$- 1 = - 1$

Step 3

Since $- 1 = - 1$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$