Exercise 20 Page 153

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 using the Properties of Equality. In this case, we start by adding 4 to both sides of the equation.

10=c/3-4+c/6

AddEqn

LHS+4=RHS+4

10+4=c/3-4+c/6+4

AddTerms

Add terms

14=c/3+c/6

Now, we can create common denominators for the fractions so that we can add them.

14=c/3+c/6

ExpandFrac

a/b=a * 2/b * 2

14=2c/6+c/6

AddFrac

Add fractions

14=2c+c/6

AddTerms

Add terms

14=3c/6

Finally, we can continue to solve using the Properties of Equality.

14=3c/6

MultEqn

LHS * 6=RHS* 6

14*6=3c/6*6

MoveRightFacToNum

a/c* b = a* b/c

14*6=3c*6/6

CancelCommonFac

Cancel out common factors

14*6=3c

Multiply

84=3c

DivEqn

.LHS /3.=.RHS /3.

84/3=3c/3

CalcQuot

Calculate quotient

28=c

RearrangeEqn

Rearrange equation

c=28

The solution to the equation is c=28. We can check our solution by substituting it into the original equation.

10=c/3-4+c/6

Substitute

c= 28

10 ? = 28/3-4+28/6

ReduceFrac

a/b=.a /2./.b /2.

10 ? = 28/3-4+14/3

AddFrac

Add fractions

10 ? = 28+14/3-4

AddTerms

Add terms

10 ? = 42/3-4

CalcQuot

Calculate quotient

10 ? = 14-4

SubTerm

Subtract term

10=10

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

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