Solve a-20=5/3(b-20)

$$a - 20 = \frac { 5 } { 3 } ( b - 20 )$$

Solve for a

$$a=\frac{5\left(b-8\right)}{3}$$

Solution Steps

Use the distributive property to multiply \frac{5}{3} by b-20.

$$a-20=\frac{5}{3}b-\frac{100}{3}$$

Add 20 to both sides.

$$a=\frac{5}{3}b-\frac{100}{3}+20$$

Add -\frac{100}{3} and 20 to get -\frac{40}{3}.

$$a=\frac{5}{3}b-\frac{40}{3}$$

Solve for b

$$b=\frac{3a}{5}+8$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{3} by b-20.

$$a-20=\frac{5}{3}b-\frac{100}{3}$$

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

$$\frac{5}{3}b-\frac{100}{3}=a-20$$

Add \frac{100}{3} to both sides.

$$\frac{5}{3}b=a-20+\frac{100}{3}$$

Add -20 and \frac{100}{3} to get \frac{40}{3}.

$$\frac{5}{3}b=a+\frac{40}{3}$$

Divide both sides of the equation by \frac{5}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{3}b}{\frac{5}{3}}=\frac{a+\frac{40}{3}}{\frac{5}{3}}$$

Dividing by \frac{5}{3} undoes the multiplication by \frac{5}{3}.

$$b=\frac{a+\frac{40}{3}}{\frac{5}{3}}$$

Divide a+\frac{40}{3} by \frac{5}{3} by multiplying a+\frac{40}{3} by the reciprocal of \frac{5}{3}.

$$b=\frac{3a}{5}+8$$