Solve 3(2-x)-2geq2x-1

$$3 ( 2 - x ) - 2 \geq 2 x - 1$$

Solve for x

$$x\leq 1$$

Solution Steps

Use the distributive property to multiply 3 by 2-x.

$$6-3x-2\geq 2x-1$$

Subtract 2 from 6 to get 4.

$$4-3x\geq 2x-1$$

Subtract 2x from both sides.

$$4-3x-2x\geq -1$$

Combine -3x and -2x to get -5x.

$$4-5x\geq -1$$

Subtract 4 from both sides.

$$-5x\geq -1-4$$

Subtract 4 from -1 to get -5.

$$-5x\geq -5$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\leq \frac{-5}{-5}$$

Divide -5 by -5 to get 1.

$$x\leq 1$$