Exercise 19 Page 463

Multiply both sides of the equation by the reciprocal of 35.

c = - 125/12

Practice makes perfect

To solve an equation, we should isolate the variable term. In this case, we will use the Multiplication Property of Equality and multiply both sides of the equation by the reciprocal of 35.

- 6 14 = 3/5c

MultEqn

LHS * 5/3=RHS* 5/3

- 6 14* 5/3 = 3/5c* 5/3

CommutativePropMult

Commutative Property of Multiplication

- 6 14* 5/3 = 3/5* 5/3* c

MultFracByInverse

a/b* b/a=1

- 6 14* 5/3 = c

▼

Simplify left-hand side

WriteDiff

Write as a difference

(- 6 - 1/4)* 5/3 = c

NumberToFrac

a = 4* a/4

(- 24/4 - 1/4)* 5/3 = c

SubFrac

Subtract fractions

- 25/4* 5/3 = c

MultFrac

Multiply fractions

- 125/12 = c

RearrangeEqn

Rearrange equation

c = - 125/12

The solution to the equation is c = - 12512. We can check our solution by substituting it into the original equation.

- 6 14 = 3/5c

Substitute

c= - 125/12

- 6 14? =3/5* ( - 125/12)

MultPosNeg

a(- b)=- a * b

- 6 14? =- 3/5* 125/12

MultFrac

Multiply fractions

- 6 14? =- 3* 125/5* 12

SplitIntoFactors

Split into factors

- 6 14? =- 3* 25* 5/5* 3* 4

CancelCommonFac

Cancel out common factors

- 6 14? =- 3* 25* 5/5* 3* 4

SimpQuot

Simplify quotient

- 6 14? =- 25/4

WriteDiff

Write as a difference

- 6 14? =- 24/4 - 1/4

CalcQuot

Calculate quotient

- 6 14? =- 6 - 1/4

SubTerm

Subtract term

- 6 14 = - 6 14 ✓

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

Subchapter links

Guided Practice p.460

Independent Practice p.461-462

H.O.T. Problems p.462

Standardized Test Practice p.462-464

Extra Practice p.463

Common Core Review p.464

Exercise 19 Page 463

Hints

Check the answer

Practice exercises

Assess your skill