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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

Chapter Review

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Exercise 33 Page 154

Apply inverse operations to isolate x.

x=pqs/q+p

Practice makes perfect

To solve the given literal equation for x, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.

x/p+x/q=s

a/b=a* 1/b

x*1/p+x*1/q=s

Factor out x

x(1/p+1/q)=s

Now, we will need to create a common denominator for the fractions, so that we can add them.

x(1/p+1/q)=s

a/b=a * q/b * q

x(q/pq+1/q)=s

a/b=a * p/b * p

x(q/pq+p/pq)=s

Add fractions

x(q+p/pq)=s

Finally, we can use the Multiplication and Division Properties of Equality to fully isolate x.

x(q+p/pq)=s

LHS * pq=RHS* pq

x(q+p/pq)* pq=s* pq

FracMultDenomToNumber

a/pq* pq = a

x(q+p)=s* pq

Multiply

x(q+p)=pqs

.LHS /(p+q).=.RHS /(p+q).

x(q+p)/(q+p)=pqs/(q+p)

CancelCommonFac

Cancel out common factors

x=pqs/(q+p)

Subchapter links

Exercises p.152-156