Solve the Inequality for x -x+23<2-2(x-8)

$- x + 23 < 2 - 2 (x - 8)$

Simplify $2 - 2 (x - 8)$ .

Simplify each term.

Apply the distributive property.

$- x + 23 < 2 - 2 x - 2 \cdot - 8$

Multiply $- 2$ by $- 8$ .

$- x + 23 < 2 - 2 x + 16$

Add $2$ and $16$ .

$- x + 23 < - 2 x + 18$

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

Add $2 x$ to both sides of the inequality.

$- x + 23 + 2 x < 18$

Add $- x$ and $2 x$ .

$x + 23 < 18$

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

Subtract $23$ from both sides of the inequality.

$x < 18 - 23$

Subtract $23$ from $18$ .

$x < - 5$

The result can be shown in multiple forms.

Inequality Form:

$x < - 5$

Interval Notation:

$(- \infty, - 5)$