Solve 1/2(c+a)=b

$$\frac { 1 } { 2 } ( c + a ) = b$$

Solve for a

$$a=-\left(c-2b\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by c+a.

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

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

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

The equation is in standard form.

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

Multiply both sides by 2.

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

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

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

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

$$a=2b-c$$

Solve for b

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

Solution Steps

Use the distributive property to multiply \frac{1}{2} by c+a.

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

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

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