Solve 4-x-2/3geq1/6x

$$4 - \frac { x - 2 } { 3 } \geq \frac { 1 } { 6 } x$$

Solve for x

$$x\leq \frac{28}{3}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6. Since 6 is positive, the inequality direction remains the same.

$$24-2\left(x-2\right)\geq 1x$$

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

$$24-2x+4\geq 1x$$

Add 24 and 4 to get 28.

$$28-2x\geq 1x$$

Subtract 1x from both sides.

$$28-2x-x\geq 0$$

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

$$28-3x\geq 0$$

Subtract 28 from both sides. Anything subtracted from zero gives its negation.

$$-3x\geq -28$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-28}{-3}$$

Fraction \frac{-28}{-3} can be simplified to \frac{28}{3} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{28}{3}$$