Solve 1/2(2m-3)=5(4/5m-1/10)

$$\frac { 1 } { 2 } ( 2 m - 3 ) = 5 ( \frac { 4 } { 5 } m - \frac { 1 } { 10 } )$$

Solve for m

$$m=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}\times 2m+\frac{1}{2}\left(-3\right)=5\left(\frac{4}{5}m-\frac{1}{10}\right)$$

Cancel out 2 and 2.

$$m+\frac{1}{2}\left(-3\right)=5\left(\frac{4}{5}m-\frac{1}{10}\right)$$

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

$$m+\frac{-3}{2}=5\left(\frac{4}{5}m-\frac{1}{10}\right)$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$m-\frac{3}{2}=5\left(\frac{4}{5}m-\frac{1}{10}\right)$$

Use the distributive property to multiply 5 by \frac{4}{5}m-\frac{1}{10}.

$$m-\frac{3}{2}=5\times \frac{4}{5}m+5\left(-\frac{1}{10}\right)$$

Cancel out 5 and 5.

$$m-\frac{3}{2}=4m+5\left(-\frac{1}{10}\right)$$

Express 5\left(-\frac{1}{10}\right) as a single fraction.

$$m-\frac{3}{2}=4m+\frac{5\left(-1\right)}{10}$$

Multiply 5 and -1 to get -5.

$$m-\frac{3}{2}=4m+\frac{-5}{10}$$

Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.

$$m-\frac{3}{2}=4m-\frac{1}{2}$$

Subtract 4m from both sides.

$$m-\frac{3}{2}-4m=-\frac{1}{2}$$

Combine m and -4m to get -3m.

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

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

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

Since -\frac{1}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

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

Add -1 and 3 to get 2.

$$-3m=\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$-3m=1$$

Divide both sides by -3.

$$m=\frac{1}{-3}$$

Fraction \frac{1}{-3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$m=-\frac{1}{3}$$