Exercise 25 Page 162

To solve the given literal equation for

b,

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

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

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LHS \cdot 2 = RHS \cdot 2

$LHS \cdot 2 = RHS \cdot 2$

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

Commutative Property of Multiplication

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

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

a + b = 2 c

$LHS - a = RHS - a$

b = 2 c - a

This corresponds to option C.