Exercise 38 Page 98

Multiply by the denominator to eliminate the fractions.

x=-8/3

Practice makes perfect

We can eliminate fractions in an equation by multiplying the entire equation by the greatest denominator. In this equation, our greatest denominator is 12. Let's try to solve for x.

x/3-7x/12=2/3

MultEqn

LHS * 12=RHS* 12

(x/3-7x/12)*12=(2/3)*12

Distr

Distribute 12

x/3*12-7x/12*12=2/3*12

FracMultDenomToNumber

a/12* 12 = a

x/3*12-7x=2/3*12

MoveRightFacToNum

a/c* b = a* b/c

x*12/3-7x=2*12/3

ReduceFrac

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

x*4/1-7x=2*4/1

DivByOne

a/1=a

x*4-7x=2*4

Multiply

4x-7x=8

SubTerm

Subtract term

-3x=8

DivEqn

.LHS /(-3).=.RHS /(-3).

x=8/-3

MoveNegDenomToFrac

Put minus sign in front of fraction

x=-8/3

Let's check our solution by substituting it into the original equation.

x/3-7x/12=2/3

Substitute

x= -8/3

( -8/3)/3-7( -8/3)/12? =2/3

MoveLeftFacToNum

a*b/c= a* b/c

(-8/3)/3-(-7*8/3)/12? =2/3

DivFracSL

.a/b /c.= a/b* c

-8/3*3-(-7*8/3*12)? =2/3

Multiply

-8/9-(-56/36)? =2/3

NegNeg

- (- a)=a

-8/9+56/36? =2/3

ExpandFrac

a/b=a * 4/b * 4

-32/36+56/36? =2/3

MoveNegFracToNum

Put minus sign in numerator

-32/36+56/36? =2/3

AddFrac

Add fractions

-32+56/36? =2/3

AddTerms

Add terms

24/36? =2/3

ReduceFrac

a/b=.a /12./.b /12.

2/3=2/3

Since the left-hand side and right-hand side are equal, we know our solution is correct.

Subchapter links

Lesson Check p.97

Practice and Problem-Solving Exercises p.98-100

Standardized Test Prep p.100

Mixed Review p.100

Exercise 38 Page 98

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