Exercise 25 Page 8

To solve the given equation for r, we need to isolate it by dividing both sides of the equation by -8. We want to divide by -8 because multiplication and division are inverse operations — they cancel each other out. This is allowed by the Division Property of Equality.

- 8r=64

DivEqn

.LHS /(- 8).=.RHS /(- 8).

- 8r/- 8=64/- 8

DivNegNeg

- a/- b=a/b

8r/8=64/-8

MoveNegDenomToFrac

Put minus sign in front of fraction

8r/8=-64/8

CalcQuot

Calculate quotient

r=- 8

We will check our solution by substituting this result back into the original equation and simplifying. If doing so results in an identity, our solution is correct.

- 8r=64

Substitute

r= - 8

\text{-} 8 ({\color{#0000FF}{\text{-} 8}}) \stackrel {?}= 64

MultNegNegOnePar

- a(- b)=a* b

8\cdot 8 \stackrel {?}= 64

Multiply

Multiply

64 = 64 ✓

Since substituting r=- 8 resulted in an identity, our solution is correct.