Exercise 8 Page 26

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other, using the Properties of Equality. In this case, we start by combining like terms.

-21a+28a-6=- 10.2

AddTerms

Add terms

7a-6=- 10.2

AddEqn

LHS+6=RHS+6

7a-6+6=- 10.2+6

AddTerms

Add terms

7a=- 4.2

DivEqn

.LHS /7.=.RHS /7.

7a/7=- 4.2/7

UseCalc

Use a calculator

a=- 0.6

Let's check our answer by substituting p=- 0.6 into the original equation. If doing so results in an identity, our solution is correct. An identity is when both sides of the equation are exactly the same.

-21a+28a-6=- 10.2

Substitute

a= - 0.6

- 21( - 0.6)+28( - 0.6)-6? =- 10.2

MultNegNegOnePar

- a(- b)=a* b

12.6+28(- 0.6)-6? =- 10.2

MultPosNeg

a(- b)=- a * b

12.6-16.8-6? =- 10.2

SubTerms

Subtract terms

- 10.2=- 10.2

Since the left-hand side and the right-hand side are equal, we know our solution is correct.