Solve 1/2left(m-1right)+5=1/3left(2m+1right)

$$\frac{ 1 }{ 2 } \left( m-1 \right) +5 = \frac{ 1 }{ 3 } \left( 2m+1 \right)$$

Solve for m

$$m=25$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by m-1.

$$\frac{1}{2}m+\frac{1}{2}\left(-1\right)+5=\frac{1}{3}\left(2m+1\right)$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$\frac{1}{2}m-\frac{1}{2}+5=\frac{1}{3}\left(2m+1\right)$$

Convert 5 to fraction \frac{10}{2}.

$$\frac{1}{2}m-\frac{1}{2}+\frac{10}{2}=\frac{1}{3}\left(2m+1\right)$$

Since -\frac{1}{2} and \frac{10}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}m+\frac{-1+10}{2}=\frac{1}{3}\left(2m+1\right)$$

Add -1 and 10 to get 9.

$$\frac{1}{2}m+\frac{9}{2}=\frac{1}{3}\left(2m+1\right)$$

Use the distributive property to multiply \frac{1}{3} by 2m+1.

$$\frac{1}{2}m+\frac{9}{2}=\frac{1}{3}\times 2m+\frac{1}{3}$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{1}{2}m+\frac{9}{2}=\frac{2}{3}m+\frac{1}{3}$$

Subtract \frac{2}{3}m from both sides.

$$\frac{1}{2}m+\frac{9}{2}-\frac{2}{3}m=\frac{1}{3}$$

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

$$-\frac{1}{6}m+\frac{9}{2}=\frac{1}{3}$$

Subtract \frac{9}{2} from both sides.

$$-\frac{1}{6}m=\frac{1}{3}-\frac{9}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{9}{2} to fractions with denominator 6.

$$-\frac{1}{6}m=\frac{2}{6}-\frac{27}{6}$$

Since \frac{2}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}m=\frac{2-27}{6}$$

Subtract 27 from 2 to get -25.

$$-\frac{1}{6}m=-\frac{25}{6}$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}.

$$m=-\frac{25}{6}\left(-6\right)$$

Express -\frac{25}{6}\left(-6\right) as a single fraction.

$$m=\frac{-25\left(-6\right)}{6}$$

Multiply -25 and -6 to get 150.

$$m=\frac{150}{6}$$

Divide 150 by 6 to get 25.

$$m=25$$