Solve -1/2(1-2x)leqx+1/3

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

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

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

Express -\frac{1}{2}\left(-2\right) as a single fraction.

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

Multiply -1 and -2 to get 2.

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

Divide 2 by 2 to get 1.

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

Subtract x from both sides.

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

Combine 1x and -x to get 0.

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

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

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

This is true for any x.

$$x\in \mathrm{R}$$