Exercise 36 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.

- 3.8g+5+2.7g=12.7

CommutativePropAdd

Commutative Property of Addition

2.7g-3.8g+5=12.7

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Subtract term

FactorOut

Factor out g

(2.7-3.8)g+5=12.7

SubTerm

Subtract term

- 1.1 g+5=12.7

SubEqn

LHS-5=RHS-5

- 1.1 g+5-5=12.7-5

SubTerm

Subtract term

- 1.1 g=7.7

DivEqn

.LHS /(- 1.1).=.RHS /(- 1.1).

- 1.1g/- 1.1 = 7.7/- 1.1

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Calculate quotient

DivNegNeg

- a/- b=a/b

1.1g/1.1 = 7.7/- 1.1

MoveNegDenomToFrac

Put minus sign in front of fraction

1.1g/1.1 =- 7.7/1.1

CalcQuot

Calculate quotient

g=- 7

The solution to the equation is g=- 7. We can check our solution by substituting it into the original equation.

- 3.8g+5+2.7g=12.7

Substitute

g= - 7

- 3.8( - 7)+5+2.7( - 7) ? = 12.7

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Simplify

MultNegNegOnePar

- a(- b)=a* b

3.8 * 7+5+2.7(- 7) ? = 12.7

MultPosNeg

a(- b)=- a * b

3.8 * 7+5+(- 2.7 * 7) ? = 12.7

Multiply

Multiply

26.6+5+(- 18.9) ? = 12.7

AddNeg

a+(- b)=a-b

26.6+5-18.9 ? = 12.7

AddSubTerms

Add and subtract terms

12.7=12.7

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