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McGraw Hill Glencoe Algebra 2, 2012

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McGraw Hill Glencoe Algebra 2, 2012 View details

3. Solving Equations

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Exercise 54 Page 23

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

x=3

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 Subtraction Property of Equality to isolate the fraction with the variable on one side.

1/x+1/4=7/12

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LHS-1/4=RHS-1/4

LHS-1/4=RHS-1/4

1/x+1/4-1/4=7/12-1/4

a/b=a * 3/b * 3

1/x+1/4-1/4=7/12-3/12

Subtract fractions

1/x=4/12

a/b=.a /4./.b /4.

1/x=1/3

Now we can continue to solve using the cross product.

1/x=1/3

Cross multiply

x*1=3*1

a * 1=a

x=3

The solution to the equation is x=3. We can check our solution by substituting it into the original equation.

1/x+1/4=7/12

x= 3

1/3+1/4? = 7/12

▼

Simplify

a/b=a * 4/b * 4

4/12+1/4 ? = 7/12

a/b=a * 3/b * 3

4/12+3/12? =7/12

Add fractions

7/12=7/12

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

Check Your Understanding p.22

Practice and Problem Solving p.22-24

H.O.T. Problems p.24

Standardized Test Practice p.25

Spiral Review p.25

Skills Review p.25