Solve 5/6x-5/3geq1/3+1/2x

$$\frac { 5 } { 6 } x - \frac { 5 } { 3 } \geq \frac { 1 } { 3 } + \frac { 1 } { 2 } x$$

Solve for x

$$x\geq 6$$

Solution Steps

Subtract \frac{1}{2}x from both sides.

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

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

$$\frac{1}{3}x-\frac{5}{3}\geq \frac{1}{3}$$

Add \frac{5}{3} to both sides.

$$\frac{1}{3}x\geq \frac{1}{3}+\frac{5}{3}$$

Since \frac{1}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x\geq \frac{1+5}{3}$$

Add 1 and 5 to get 6.

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

Divide 6 by 3 to get 2.

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

Multiply both sides by 3, the reciprocal of \frac{1}{3}. Since \frac{1}{3} is positive, the inequality direction remains the same.

$$x\geq 2\times 3$$

Multiply 2 and 3 to get 6.

$$x\geq 6$$