Solve the Inequality for x -2(x-2)<=x+1

$- 2 (x - 2) \leq x + 1$

Simplify $- 2 (x - 2)$ .

Rewrite.

$0 + 0 - 2 (x - 2) \leq x + 1$

Simplify by adding zeros.

$- 2 (x - 2) \leq x + 1$

Apply the distributive property.

$- 2 x - 2 \cdot - 2 \leq x + 1$

Multiply $- 2$ by $- 2$ .

$- 2 x + 4 \leq x + 1$

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

Subtract $x$ from both sides of the inequality.

$- 2 x + 4 - x \leq 1$

Subtract $x$ from $- 2 x$ .

$- 3 x + 4 \leq 1$

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

Subtract $4$ from both sides of the inequality.

$- 3 x \leq 1 - 4$

Subtract $4$ from $1$ .

$- 3 x \leq - 3$

Divide each term in $- 3 x \leq - 3$ by $- 3$ and simplify.

Divide each term in $- 3 x \leq - 3$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{- 3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{- 3}{- 3}$

Divide $x$ by $1$ .

$x \geq \frac{- 3}{- 3}$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x \geq 1$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 1$

Interval Notation:

$[1, \infty)$

Solve the Inequality for x -2(x-2)<=x+1

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