Exercise 51 Page 121

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

Practice makes perfect

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, we will start by using the Addition Property of Equality.

-2/3x-8=-12

AddEqn

LHS+8=RHS+8

-2/3x-8+8=-12+8

AddTerms

Add terms

-2/3x=-4

MoveNegFracToDenom

Put minus sign in denominator

2/-3x=-4

MoveRightFacToNum

a/c* b = a* b/c

2x/-3=-4

MultEqn

LHS * (-3)=RHS* (-3)

2x=-4(-3)

MultNegNegOnePar

- a(- b)=a* b

2x=12

DivEqn

.LHS /2.=.RHS /2.

2x/2=12/2

CalcQuot

Calculate quotient

x=6

The solution to the equation is x=6. We can check our solution by substituting it into the original equation.

-2/3x-8=-12

Substitute

x= 6

-2/3( 6)-8? =-12

MoveRightFacToNum

a/c* b = a* b/c

-2*6/3-8? =-12

Multiply

-12/3-8? =-12

CalcQuot

Calculate quotient

-4-8? =-12

SubTerm

Subtract term

-12=-12

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

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