Solve for b s=n/2(a+b)

$s = \frac{n}{2} (a + b)$

Step 1

Rewrite the equation as $\frac{n}{2} \cdot (a + b) = s$ .

$\frac{n}{2} \cdot (a + b) = s$

Step 2

Multiply each term in $\frac{n}{2} \cdot (a + b) = s$ by $\frac{2}{n}$ to eliminate the fractions.

Multiply each term in $\frac{n}{2} \cdot (a + b) = s$ by $\frac{2}{n}$ .

$\frac{n}{2} \cdot (a + b) \frac{2}{n} = s \frac{2}{n}$

Simplify the left side.

Simplify terms.

Apply the distributive property.

$(\frac{n}{2} a + \frac{n}{2} b) \frac{2}{n} = s \frac{2}{n}$

Combine $\frac{n}{2}$ and $a$ .

$(\frac{n a}{2} + \frac{n}{2} b) \frac{2}{n} = s \frac{2}{n}$

Combine $\frac{n}{2}$ and $b$ .

$(\frac{n a}{2} + \frac{n b}{2}) \frac{2}{n} = s \frac{2}{n}$

Multiply $\frac{n a}{2} + \frac{n b}{2}$ by $\frac{2}{n}$ .

$\frac{(\frac{n a}{2} + \frac{n b}{2}) \cdot 2}{n} = s \frac{2}{n}$

Simplify the numerator.

Combine the numerators over the common denominator.

$\frac{\frac{n a + n b}{2} \cdot 2}{n} = s \frac{2}{n}$

Factor $n$ out of $n a + n b$ .

Factor $n$ out of $n a$ .

$\frac{\frac{n (a) + n b}{2} \cdot 2}{n} = s \frac{2}{n}$

Factor $n$ out of $n b$ .

$\frac{\frac{n (a) + n (b)}{2} \cdot 2}{n} = s \frac{2}{n}$

Factor $n$ out of $n (a) + n (b)$ .

$\frac{\frac{n (a + b)}{2} \cdot 2}{n} = s \frac{2}{n}$

Combine $\frac{n (a + b)}{2}$ and $2$ .

$\frac{\frac{n (a + b) \cdot 2}{2}}{n} = s \frac{2}{n}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{n (a + b) \cdot 2}{2}$ by cancelling the common factors.

Cancel the common factor.

$\frac{\frac{n (a + b) \cdot 2}{2}}{n} = s \frac{2}{n}$

Rewrite the expression.

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

Divide $n (a + b)$ by $1$ .

$\frac{n (a + b)}{n} = s \frac{2}{n}$

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{n (a + b)}{n} = s \frac{2}{n}$

Divide $a + b$ by $1$ .

$a + b = s \frac{2}{n}$

Simplify the right side.

Combine $s$ and $\frac{2}{n}$ .

$a + b = \frac{s \cdot 2}{n}$

Move $2$ to the left of $s$ .

$a + b = \frac{2 s}{n}$

Step 3

Subtract $a$ from both sides of the equation.

$b = \frac{2 s}{n} - a$

Solve for b s=n/2(a+b)

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