Exercise 11 Page 98

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

2 67

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using the Properties of Equality. In this case, the variable term is already on the left-hand side of the equation, so we will start by combining like terms and then isolating d-term.

72+4-14d=36

AddTerms

Add terms

76-14d=36

SubEqn

LHS-76=RHS-76

76-14d-76=36-76

SubTerms

Subtract terms

- 14d= - 40

DivEqn

.LHS /(- 14).=.RHS /(- 14).

- 14d/- 14= - 40/- 14

MovePartNumRight

a* b/c=a/c* b

- 14/- 14d= - 40/- 14

DivNegNeg

- a/- b=a/b

d= 40/14

ReduceFrac

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

d= 20/7

Since 20 and 7 share no common factors, this is as simplified as our solution can get. We can check our solution by substituting it into the original equation.

72+4-14d=36

Substitute

d= 20/7

72+4-14( 20/7)? =36

▼

Evaluate left-hand side

MoveLeftFacToNum

a*b/c= a* b/c

72+4-14* 20/7? =36

Multiply

72+4-280/7? =36

CalcQuot

Calculate quotient

72+4-40 ? =36

AddSubTerms

Add and subtract terms

36=36

Since the left-hand side is equal to the right-hand side, our solution is correct. Although d= 207 is a perfectly valid answer, we can also rewrite it as a mixed number.

d= 20/7

WriteSum

Write as a sum

d= 14+6/7

WriteSumFrac

Write as a sum of fractions

d= 14/7+6/7

CalcQuot

Calculate quotient

d = 2 + 6/7

Rewrite

Rewrite 2 + 6/7 as 2 67