Solve 1/3-2x-1/6geq2x+1/6

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

Solve for x

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

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.

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

To find the opposite of 2x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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

Add 2 and 1 to get 3.

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

Subtract 2x from both sides.

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

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

$$3-4x\geq 1$$

Subtract 3 from both sides.

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

Subtract 3 from 1 to get -2.

$$-4x\geq -2$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\leq \frac{-2}{-4}$$

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

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