Solve 1/2xleq1/3(x-2)

$$\frac { 1 } { 2 } x \leq \frac { 1 } { 3 } ( x - 2 )$$

Solve for x

$$x\leq -4$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by x-2.

$$\frac{1}{2}x\leq \frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

$$\frac{1}{2}x\leq \frac{1}{3}x+\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{1}{2}x\leq \frac{1}{3}x-\frac{2}{3}$$

Subtract \frac{1}{3}x from both sides.

$$\frac{1}{2}x-\frac{1}{3}x\leq -\frac{2}{3}$$

Combine \frac{1}{2}x and -\frac{1}{3}x to get \frac{1}{6}x.

$$\frac{1}{6}x\leq -\frac{2}{3}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}. Since \frac{1}{6} is positive, the inequality direction remains the same.

$$x\leq -\frac{2}{3}\times 6$$

Express -\frac{2}{3}\times 6 as a single fraction.

$$x\leq \frac{-2\times 6}{3}$$

Multiply -2 and 6 to get -12.

$$x\leq \frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$x\leq -4$$