Solve for a S=n/2(a+L)

$S = \frac{n}{2} (a + L)$

Step 1

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

$\frac{n}{2} \cdot (a + L) = S$

Step 2

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

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

$\frac{n}{2} \cdot (a + L) \frac{2}{n} = S \frac{2}{n}$

Simplify the left side.

Simplify terms.

Apply the distributive property.

$(\frac{n}{2} a + \frac{n}{2} L) \frac{2}{n} = S \frac{2}{n}$

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

$(\frac{n a}{2} + \frac{n}{2} L) \frac{2}{n} = S \frac{2}{n}$

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

$(\frac{n a}{2} + \frac{n L}{2}) \frac{2}{n} = S \frac{2}{n}$

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

$\frac{(\frac{n a}{2} + \frac{n L}{2}) \cdot 2}{n} = S \frac{2}{n}$

Simplify the numerator.

Combine the numerators over the common denominator.

$\frac{\frac{n a + n L}{2} \cdot 2}{n} = S \frac{2}{n}$

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

Factor $n$ out of $n a$ .

$\frac{\frac{n (a) + n L}{2} \cdot 2}{n} = S \frac{2}{n}$

Factor $n$ out of $n L$ .

$\frac{\frac{n (a) + n (L)}{2} \cdot 2}{n} = S \frac{2}{n}$

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

$\frac{\frac{n (a + L)}{2} \cdot 2}{n} = S \frac{2}{n}$

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

$\frac{\frac{n (a + L) \cdot 2}{2}}{n} = S \frac{2}{n}$

Reduce the expression by cancelling the common factors.

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

Cancel the common factor.

$\frac{\frac{n (a + L) \cdot 2}{2}}{n} = S \frac{2}{n}$

Rewrite the expression.

$\frac{\frac{n (a + L)}{1}}{n} = S \frac{2}{n}$

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

$\frac{n (a + L)}{n} = S \frac{2}{n}$

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{n (a + L)}{n} = S \frac{2}{n}$

Divide $a + L$ by $1$ .

$a + L = S \frac{2}{n}$

Simplify the right side.

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

$a + L = \frac{S \cdot 2}{n}$

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

$a + L = \frac{2 S}{n}$

Step 3

Subtract $L$ from both sides of the equation.

$a = \frac{2 S}{n} - L$

Solve for a S=n/2(a+L)

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