Solve S=a+b/2

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

Solve for a

$$a=2S-b$$

Steps for Solving Linear Equation

Divide each term of a+b by 2 to get \frac{1}{2}a+\frac{1}{2}b.

$$S=\frac{1}{2}a+\frac{1}{2}b$$

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

$$\frac{1}{2}a+\frac{1}{2}b=S$$

Subtract \frac{1}{2}b from both sides.

$$\frac{1}{2}a=S-\frac{1}{2}b$$

The equation is in standard form.

$$\frac{1}{2}a=-\frac{b}{2}+S$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}a}{\frac{1}{2}}=\frac{-\frac{b}{2}+S}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$a=\frac{-\frac{b}{2}+S}{\frac{1}{2}}$$

Divide S-\frac{b}{2} by \frac{1}{2} by multiplying S-\frac{b}{2} by the reciprocal of \frac{1}{2}.

$$a=2S-b$$

Solve for S

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

Solution Steps

Divide each term of a+b by 2 to get \frac{1}{2}a+\frac{1}{2}b.

$$S=\frac{1}{2}a+\frac{1}{2}b$$