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

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

Solution Steps

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

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

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

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

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

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

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

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

Add 8 and 10 to get 18.

$$\frac{18}{3}-3m\geq \frac{8}{3}-2m+m-\frac{10}{3}$$

Divide 18 by 3 to get 6.

$$6-3m\geq \frac{8}{3}-2m+m-\frac{10}{3}$$

Combine -2m and m to get -m.

$$6-3m\geq \frac{8}{3}-m-\frac{10}{3}$$

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

$$6-3m\geq \frac{8-10}{3}-m$$

Subtract 10 from 8 to get -2.

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

Add m to both sides.

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

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

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

Subtract 6 from both sides.

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

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

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

Since -\frac{2}{3} and \frac{18}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 18 from -2 to get -20.

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

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$m\leq \frac{-\frac{20}{3}}{-2}$$

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

$$m\leq \frac{-20}{3\left(-2\right)}$$

Multiply 3 and -2 to get -6.

$$m\leq \frac{-20}{-6}$$

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

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