Solve a+b/2=b+2/3

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

Solve for a

$$a=\frac{4-b}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(a+b\right)=2\left(b+2\right)$$

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

$$3a+3b=2\left(b+2\right)$$

Use the distributive property to multiply 2 by b+2.

$$3a+3b=2b+4$$

Subtract 3b from both sides.

$$3a=2b+4-3b$$

Combine 2b and -3b to get -b.

$$3a=-b+4$$

The equation is in standard form.

$$3a=4-b$$

Divide both sides by 3.

$$\frac{3a}{3}=\frac{4-b}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$a=\frac{4-b}{3}$$

Solve for b

$$b=4-3a$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(a+b\right)=2\left(b+2\right)$$

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

$$3a+3b=2\left(b+2\right)$$

Use the distributive property to multiply 2 by b+2.

$$3a+3b=2b+4$$

Subtract 2b from both sides.

$$3a+3b-2b=4$$

Combine 3b and -2b to get b.

$$3a+b=4$$

Subtract 3a from both sides.

$$b=4-3a$$