Solve 7/2left(m+12right)=5/2left(20+mright)

$$\frac{ 7 }{ 2 } \left( m+12 \right) = \frac{ 5 }{ 2 } \left( 20+m \right)$$

Solve for m

$$m=8$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{2} by m+12.

$$\frac{7}{2}m+\frac{7}{2}\times 12=\frac{5}{2}\left(20+m\right)$$

Express \frac{7}{2}\times 12 as a single fraction.

$$\frac{7}{2}m+\frac{7\times 12}{2}=\frac{5}{2}\left(20+m\right)$$

Multiply 7 and 12 to get 84.

$$\frac{7}{2}m+\frac{84}{2}=\frac{5}{2}\left(20+m\right)$$

Divide 84 by 2 to get 42.

$$\frac{7}{2}m+42=\frac{5}{2}\left(20+m\right)$$

Use the distributive property to multiply \frac{5}{2} by 20+m.

$$\frac{7}{2}m+42=\frac{5}{2}\times 20+\frac{5}{2}m$$

Express \frac{5}{2}\times 20 as a single fraction.

$$\frac{7}{2}m+42=\frac{5\times 20}{2}+\frac{5}{2}m$$

Multiply 5 and 20 to get 100.

$$\frac{7}{2}m+42=\frac{100}{2}+\frac{5}{2}m$$

Divide 100 by 2 to get 50.

$$\frac{7}{2}m+42=50+\frac{5}{2}m$$

Subtract \frac{5}{2}m from both sides.

$$\frac{7}{2}m+42-\frac{5}{2}m=50$$

Combine \frac{7}{2}m and -\frac{5}{2}m to get m.

$$m+42=50$$

Subtract 42 from both sides.

$$m=50-42$$

Subtract 42 from 50 to get 8.

$$m=8$$