Solve -(x-2)leq2-(3x+2)

$$-(x-2) \leq 2-(3x+2)$$

Solve for x

$$x\leq -1$$

Solution Steps

To find the opposite of x-2, find the opposite of each term.

$$-x-\left(-2\right)\leq 2-\left(3x+2\right)$$

The opposite of -2 is 2.

$$-x+2\leq 2-\left(3x+2\right)$$

To find the opposite of 3x+2, find the opposite of each term.

$$-x+2\leq 2-3x-2$$

Subtract 2 from 2 to get 0.

$$-x+2\leq -3x$$

Add 3x to both sides.

$$-x+2+3x\leq 0$$

Combine -x and 3x to get 2x.

$$2x+2\leq 0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$2x\leq -2$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x\leq \frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$x\leq -1$$