Exercise 70 Page 162

To solve the given formula for

A,

we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.

S = \frac{n}{2} (A + t)

$LHS \cdot 2 = RHS \cdot 2$

2 S = 2 \cdot \frac{n}{2} (A + t)

$2 \cdot \frac{a}{2} = a$

2 S = n (A + t)

$LHS / n = RHS / n$

\frac{2 S}{n} = \frac{n ( A + t )}{n}

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Simplify right-hand side

$\frac{a}{b} = \frac{a / n}{b / n}$

\frac{2 S}{n} = \frac{A + t}{1}

$\frac{a}{1} = a$

\frac{2 S}{n} = A + t

$LHS - t = RHS - t$

\frac{2 S}{n} - t = A

Rearrange equation

A = \frac{2 S}{n} - t