Exercise 26 Page 106

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 need to start by using the Distributive Property to simplify the left-hand side of the equation. Now we can continue to solve using the Properties of Equality.

17g-20=1-g

AddEqn

LHS+g=RHS+g

17g-20+g=1-g+g

AddTerms

Add terms

18g-20=1

AddEqn

LHS+20=RHS+20

18g-20+20=1+20

AddTerms

Add terms

18g=21

DivEqn

.LHS /18.=.RHS /18.

18g/18=21/18

CalcQuot

Calculate quotient

g=21/18

ReduceFrac

a/b=.a /3./.b /3.

g=7/6

The solution to the equation is g= 76. We can check our solution by substituting it into the original equation.

5g+4(-5+3g)=1-g

Substitute

g= 7/6

5( 7/6)+4(-5+3( 7/6))? =1- 7/6

▼

Simplify

MoveLeftFacToNum

a*b/c= a* b/c

35/6+4(-5+21/6)? =1-7/6

NumberToFrac

a = 6* a/6

35/6+4(-5* 6/6+21/6)? =6* 1/6-7/6

Multiply

Multiply

35/6+4(-30/6+21/6)? =6/6-7/6

AddSubFrac

Add and subtract fractions

35/6+4(-9/6)? =-1/6

MoveLeftFacToNum

a*b/c= a* b/c

35/6+-36/6? =-1/6

AddFrac

Add fractions

-1/6=-1/6 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct. We can also represent our answer as a mixed number.

7/6

▼

Write as mixed number

Rewrite

Rewrite 7 as 6+1

6+1/6

AddPar

Add parentheses

(6+1/6)

WriteSumFrac

Write as a sum of fractions

(6/6+1/6)

QuotOne

a/a=1

(1+1/6)

AddTerms

Add terms

(1 16)

RemovePar

Remove parentheses

1 16