Exercise 35 Page 144

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 side using the Properties of Equality. In this case, the only variable terms are already on the left-hand side of the equation, so we will start by combining them.

- 8d-5d+7d=72

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Add and subtract terms

FactorOut

Factor out d

(- 8-5+7)d=72

AddSubTerms

Add and subtract terms

- 6d= 72

DivEqn

.LHS /(- 6).=.RHS /(- 6).

- 6d/- 6 = 72/- 6

DivNegNeg

- a/- b=a/b

6d/6 = 72/- 6

MoveNegDenomToFrac

Put minus sign in front of fraction

6d/6 = - 72/6

CalcQuot

Calculate quotient

d=- 12

The solution to the equation is d=- 12. We can check our solution by substituting it into the original equation.

- 8d-5d+7d=72

Substitute

d= - 12

- 8( - 12)-5( - 12)+7( - 12) ? = 72

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Simplify

MultNegNegOnePar

- a(- b)=a* b

8* 12-5(- 12) + 7(- 12)? = 72

MultPosNeg

a(- b)=- a * b

8* 12-(- 5 * 12)+ (- 7 * 12) ? = 72

Multiply

Multiply

96-(- 60)+ (- 84) ? = 72

SubNeg

a-(- b)=a+b

96+60+ (- 84) ? = 72

AddNeg

a+(- b)=a-b

96+60-84 ? = 72

AddSubTerms

Add and subtract terms

72=72

Since the left-hand side is equal to the right-hand side, our solution is correct.