Solve x/3+x/6geqx/4+230

$$\frac { x } { 3 } + \frac { x } { 6 } \geq \frac { x } { 4 } + 230$$

Solve for x

$$x\geq 920$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,6,4. Since 12 is positive, the inequality direction remains the same.

$$4x+2x\geq 3x+2760$$

Combine 4x and 2x to get 6x.

$$6x\geq 3x+2760$$

Subtract 3x from both sides.

$$6x-3x\geq 2760$$

Combine 6x and -3x to get 3x.

$$3x\geq 2760$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x\geq \frac{2760}{3}$$

Divide 2760 by 3 to get 920.

$$x\geq 920$$