Solve 5/6x-1/2xleq3/8x-1/6

$$\frac { 5 } { 6 } x - \frac { 1 } { 2 } x \leq \frac { 3 } { 8 } x - \frac { 1 } { 6 }$$

Solve for x

$$x\geq 4$$

Solution Steps

Combine \frac{5}{6}x and -\frac{1}{2}x to get \frac{1}{3}x.

$$\frac{1}{3}x\leq \frac{3}{8}x-\frac{1}{6}$$

Subtract \frac{3}{8}x from both sides.

$$\frac{1}{3}x-\frac{3}{8}x\leq -\frac{1}{6}$$

Combine \frac{1}{3}x and -\frac{3}{8}x to get -\frac{1}{24}x.

$$-\frac{1}{24}x\leq -\frac{1}{6}$$

Multiply both sides by -24, the reciprocal of -\frac{1}{24}. Since -\frac{1}{24} is negative, the inequality direction is changed.

$$x\geq -\frac{1}{6}\left(-24\right)$$

Express -\frac{1}{6}\left(-24\right) as a single fraction.

$$x\geq \frac{-\left(-24\right)}{6}$$

Multiply -1 and -24 to get 24.

$$x\geq \frac{24}{6}$$

Divide 24 by 6 to get 4.

$$x\geq 4$$