Solve 2(3-x)geq4x+2

$$2(3-x) \geq 4x+2$$

Solve for x

$$x\leq \frac{2}{3}$$

Solution Steps

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

$$6-2x\geq 4x+2$$

Subtract 4x from both sides.

$$6-2x-4x\geq 2$$

Combine -2x and -4x to get -6x.

$$6-6x\geq 2$$

Subtract 6 from both sides.

$$-6x\geq 2-6$$

Subtract 6 from 2 to get -4.

$$-6x\geq -4$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x\leq \frac{-4}{-6}$$

Reduce the fraction \frac{-4}{-6} to lowest terms by extracting and canceling out -2.

$$x\leq \frac{2}{3}$$