Solve x/3-1/6leq3x/4

$$\frac{ x }{ 3 } - \frac{ 1 }{ 6 } \leq \frac{ 3x }{ 4 }$$

Solve for x

$$x\geq -\frac{2}{5}$$

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.

$$4x-2\leq 3\times 3x$$

Multiply 3 and 3 to get 9.

$$4x-2\leq 9x$$

Subtract 9x from both sides.

$$4x-2-9x\leq 0$$

Combine 4x and -9x to get -5x.

$$-5x-2\leq 0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-5x\leq 2$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq -\frac{2}{5}$$