Exercise 2 Page 460

To solve the equation, we have to isolate b on one side. Using the Division Property of Equality, we will divide both sides of the equation by - 2.5. This will eliminate the multiplication and isolate b.

- 2.5b = 20.5

DivEqn

.LHS /- 2.5.=.RHS /- 2.5.

- 2.5b/- 2.5 = 20.5/- 2.5

CancelCommonFac

Cancel out common factors

- 2.5b/- 2.5 = 20.5/- 2.5

SimpQuot

Simplify quotient

b = 20.5/- 2.5

MoveNegDenomToFrac

Put minus sign in front of fraction

b = - 20.5/2.5

CalcQuot

Calculate quotient

b = - 8.2

To check that this solution is correct, let's substitute b = - 8.2 into the original equation and simplify.

- 2.5b = 20.5

Substitute

b= - 8.2

- 2.5( - 8.2)? = 20.5

MultNegNegOnePar

- a(- b)=a* b

20.5 = 20.5 ✓

Since the left-hand side and right-hand side are equal, b = - 8.2 is the correct solution.