Solve 4left(b+1right)=5left(a+2right)

$$4 \left( b+1 \right) = 5 \left( a+2 \right)$$

Solve for a

$$a=\frac{4b-6}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by b+1.

$$4b+4=5\left(a+2\right)$$

Use the distributive property to multiply 5 by a+2.

$$4b+4=5a+10$$

Swap sides so that all variable terms are on the left hand side.

$$5a+10=4b+4$$

Subtract 10 from both sides.

$$5a=4b+4-10$$

Subtract 10 from 4 to get -6.

$$5a=4b-6$$

Divide both sides by 5.

$$\frac{5a}{5}=\frac{4b-6}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$a=\frac{4b-6}{5}$$

Solve for b

$$b=\frac{5a}{4}+\frac{3}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by b+1.

$$4b+4=5\left(a+2\right)$$

Use the distributive property to multiply 5 by a+2.

$$4b+4=5a+10$$

Subtract 4 from both sides.

$$4b=5a+10-4$$

Subtract 4 from 10 to get 6.

$$4b=5a+6$$

Divide both sides by 4.

$$\frac{4b}{4}=\frac{5a+6}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$b=\frac{5a+6}{4}$$

Divide 5a+6 by 4.

$$b=\frac{5a}{4}+\frac{3}{2}$$