Exercise 46 Page 98

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

28 12

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, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

2/3(c-18)=7

Distr

Distribute 2/3

(2/3)c-(2/3)18=7

MoveRightFacToNum

a/c* b = a* b/c

2c/3-36/3=7

CalcQuot

Calculate quotient

2c/3-12=7

AddEqn

LHS+12=RHS+12

2c/3=19

MultEqn

LHS * 3=RHS* 3

2c=57

DivEqn

.LHS /2.=.RHS /2.

c=57/2

There are no common factors between 57 and 2 so the fraction is as simplified as possible. The solution to the equation is c= 572. Although it is a valid answer, we can also rewrite it in a mixed number.

c=57/2

Rewrite

Rewrite 57 as 28*2+1

c=28*2+1/2

WriteSumFrac

Write as a sum of fractions

c=28*2/2+1/2

CalcQuot

Calculate quotient

c=28+1/2

Rewrite

Rewrite 28+1/2 as 28 12