Solve 8/3-2m+m-10/3geq8/3-2m-(m-10/3)

$$\frac { 8 } { 3 } - 2 m + m - \frac { 10 } { 3 } \geq \frac { 8 } { 3 } - 2 m - ( m - \frac { 10 } { 3 } )$$

Solve for m

$$m\geq \frac{10}{3}$$

Solution Steps

Combine -2m and m to get -m.

$$\frac{8}{3}-m-\frac{10}{3}\geq \frac{8}{3}-2m-\left(m-\frac{10}{3}\right)$$

Since \frac{8}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-10}{3}-m\geq \frac{8}{3}-2m-\left(m-\frac{10}{3}\right)$$

Subtract 10 from 8 to get -2.

$$-\frac{2}{3}-m\geq \frac{8}{3}-2m-\left(m-\frac{10}{3}\right)$$

To find the opposite of m-\frac{10}{3}, find the opposite of each term.

$$-\frac{2}{3}-m\geq \frac{8}{3}-2m-m-\left(-\frac{10}{3}\right)$$

The opposite of -\frac{10}{3} is \frac{10}{3}.

$$-\frac{2}{3}-m\geq \frac{8}{3}-2m-m+\frac{10}{3}$$

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

$$-\frac{2}{3}-m\geq \frac{8}{3}-3m+\frac{10}{3}$$

Since \frac{8}{3} and \frac{10}{3} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}-m\geq \frac{8+10}{3}-3m$$

Add 8 and 10 to get 18.

$$-\frac{2}{3}-m\geq \frac{18}{3}-3m$$

Divide 18 by 3 to get 6.

$$-\frac{2}{3}-m\geq 6-3m$$

Add 3m to both sides.

$$-\frac{2}{3}-m+3m\geq 6$$

Combine -m and 3m to get 2m.

$$-\frac{2}{3}+2m\geq 6$$

Add \frac{2}{3} to both sides.

$$2m\geq 6+\frac{2}{3}$$

Convert 6 to fraction \frac{18}{3}.

$$2m\geq \frac{18}{3}+\frac{2}{3}$$

Since \frac{18}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$2m\geq \frac{18+2}{3}$$

Add 18 and 2 to get 20.

$$2m\geq \frac{20}{3}$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$m\geq \frac{\frac{20}{3}}{2}$$

Express \frac{\frac{20}{3}}{2} as a single fraction.

$$m\geq \frac{20}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$m\geq \frac{20}{6}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$m\geq \frac{10}{3}$$