Solve x/3+1/6geqx/2

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

Solve for x

$$x\leq 1$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6,2. Since 6 is positive, the inequality direction remains the same.

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

Subtract 3x from both sides.

$$2x+1-3x\geq 0$$

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

$$-x+1\geq 0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-x\geq -1$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

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

Divide -1 by -1 to get 1.

$$x\leq 1$$