Solve 3(a+b-2)=1/3(4a+3)

$$3 ( a + b - 2 ) = \frac { 1 } { 3 } ( 4 a + 3 )$$

Solve for a

$$a=\frac{21-9b}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by a+b-2.

$$3a+3b-6=\frac{1}{3}\left(4a+3\right)$$

Use the distributive property to multiply \frac{1}{3} by 4a+3.

$$3a+3b-6=\frac{4}{3}a+1$$

Subtract \frac{4}{3}a from both sides.

$$3a+3b-6-\frac{4}{3}a=1$$

Combine 3a and -\frac{4}{3}a to get \frac{5}{3}a.

$$\frac{5}{3}a+3b-6=1$$

Subtract 3b from both sides.

$$\frac{5}{3}a-6=1-3b$$

Add 6 to both sides.

$$\frac{5}{3}a=1-3b+6$$

Add 1 and 6 to get 7.

$$\frac{5}{3}a=7-3b$$

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

$$\frac{\frac{5}{3}a}{\frac{5}{3}}=\frac{7-3b}{\frac{5}{3}}$$

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

$$a=\frac{7-3b}{\frac{5}{3}}$$

Divide 7-3b by \frac{5}{3} by multiplying 7-3b by the reciprocal of \frac{5}{3}.

$$a=\frac{21-9b}{5}$$

Solve for b

$$b=-\frac{5a}{9}+\frac{7}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by a+b-2.

$$3a+3b-6=\frac{1}{3}\left(4a+3\right)$$

Use the distributive property to multiply \frac{1}{3} by 4a+3.

$$3a+3b-6=\frac{4}{3}a+1$$

Subtract 3a from both sides.

$$3b-6=\frac{4}{3}a+1-3a$$

Combine \frac{4}{3}a and -3a to get -\frac{5}{3}a.

$$3b-6=-\frac{5}{3}a+1$$

Add 6 to both sides.

$$3b=-\frac{5}{3}a+1+6$$

Add 1 and 6 to get 7.

$$3b=-\frac{5}{3}a+7$$

The equation is in standard form.

$$3b=-\frac{5a}{3}+7$$

Divide both sides by 3.

$$\frac{3b}{3}=\frac{-\frac{5a}{3}+7}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$b=\frac{-\frac{5a}{3}+7}{3}$$

Divide -\frac{5a}{3}+7 by 3.

$$b=-\frac{5a}{9}+\frac{7}{3}$$