Solve the Inequality for x -20+x>=-(20-x)

$- 20 + x \geq - (20 - x)$

Step 1

Simplify $- (20 - x)$ .

Rewrite.

$- 20 + x \geq 0 + 0 - (20 - x)$

Simplify by adding zeros.

$- 20 + x \geq - (20 - x)$

Apply the distributive property.

$- 20 + x \geq - 1 \cdot 20 - - x$

Multiply $- 1$ by $20$ .

$- 20 + x \geq - 20 - - x$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$- 20 + x \geq - 20 + 1 x$

Multiply $x$ by $1$ .

$- 20 + x \geq - 20 + x$

Step 2

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

Subtract $x$ from both sides of the inequality.

$- 20 + x - x \geq - 20$

Combine the opposite terms in $- 20 + x - x$ .

Subtract $x$ from $x$ .

$- 20 + 0 \geq - 20$

Add $- 20$ and $0$ .

$- 20 \geq - 20$

Step 3

Since $- 20 = - 20$ , the equation will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$