Exercise 41 Page 512

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 should use the Addition Property of Equality and the Division Property of Equality to isolate the variable.

14n -32=22

AddEqn

LHS+32=RHS+32

14n = 54

DivEqn

.LHS /14.=.RHS /14.

n = 54/14

ReduceFrac

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

n = 27/7

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Write fraction as a mixed number

WriteSum

Write as a sum

n = 21+6/7

WriteSumFrac

Write as a sum of fractions

n = 21/7 + 6/7

CalcQuot

Calculate quotient

n = 3 + 6/7

AddTerms

Add terms

n = 3 67

The solution to the equation is n = 3 67. We can check our solution by substituting it into the original equation.

14n -32=22

Substitute

n= 3 67

14( 3 67) - 32 ? = 22

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Write mixed number as a fraction

MixedToFrac

a bc=a* c+b/c

14( 3 * 7 + 6/7 ) - 32 ? = 22

Multiply

Multiply

14( 21 + 6/7 ) - 32 ? = 22

\AddTerm

14( 27/7 ) - 32 ? = 22

MoveLeftFacToNum

a*b/c= a* b/c

378/7- 32 ? = 22

CalcQuot

Calculate quotient

54 - 32 ? = 22

SubTerm

Subtract term

22 = 22 ✓

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