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Pearson Algebra 1 Common Core, 2011 View details

1. Solving One-Step Equations

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Exercise 55 Page 86

We will need to create common denominator for the fractions.

-1/21

Practice makes perfect

To solve this equation, we need to isolate a on one side. To do this, we will use the Subtraction Property of Equality.

2/7=1/3+a

SubEqn

LHS-1/3=RHS-1/3

2/7- 1/3=1/3+a- 1/3

AssociativePropAdd

Associative Property of Addition

2/7-1/3=1/3-1/3+a

SubFrac

Subtract fractions

2/7-1/3=a

RearrangeEqn

Rearrange equation

a=2/7-1/3

Now let's subtract these fractions by creating a common denominator and simplifying. It will not necessarily be the lowest common denominator, but an easy way to create a common denominator between two fractions is to multiply the numerator and denominator of each fraction by the other denominator.

a/b+c/d = a/b*d/d+c/d*b/b Let's do it.

a=2/7-1/3

▼

Subtract fractions

ExpandFrac

a/b=a * 3/b * 3

a=2* 3/7* 3-1/3

ExpandFrac

a/b=a * 7/b * 7

a=2* 3/7* 3-1* 7/3* 7

Multiply

a=6/21-7/21

SubFrac

Subtract fractions

a=6-7/21

SubTerm

Subtract term

a=- 1/21

MoveNegNumToFrac

Put minus sign in front of fraction

a=-1/21

We've found that a=- 121 is the solution to the equation. To check our answer, we will substitute our solution back into the original equation and confirm that it creates an identity.

2/7=1/3+a

Substitute

a= -1/21

2/7? =1/3+( -1/21)

▼

Simplify fractions

AddNeg

a+(- b)=a-b

2/7? =1/3-1/21

ExpandFrac

a/b=a * 7/b * 7

2/7? =1* 7/3* 7-1/21