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 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Equations with Fractions

After studying this lesson, you will be able to:

• Solve equations containing fractions.

To Solve Equations containing fractions:

Clear out the fractions by multiplying the ENTIRE equation by the common denominator.

Example 1 This equation contains 2 fractions. In order to clear the fractions, we need to multiply the ENTIRE equation by the common denominator. Since both denominators are 5, that will be the common denominator. Since 5 is the common denominator, we multiply EVERY TERM by 5 3x + 15 = 1x -35 Notice that where we have fractions the fives cancel out each other leaving us with no fractions. 3x + 15 - 1x = 1x -35 - 1x We subtract 1x from each side in order to get the variables together. 2x + 15 = -35 After collecting the 3x - 1x we have this equation which needs to be solved. 2x + 15 - 15 = -35 - 15 "Undo" the +15 by subtracting 15 from each sideThis gives us 2x = -50 "Undo" the 2 times x by dividing each side by 2 x = -25 This gives us the solution

Check by substituting -25 into the equation where we first cleared out the fractions

3 ( -25 ) + 15 = 1 (-25 ) - 35

-75 + 15 = -25 - 35

-60 = -60

Example 2 This equation contains 2 fractions. In order to clear the fractions, we need to multiply the ENTIRE equation by the common denominator. Since the denominators are 5 and 2, the common denominator will be 10. Since 10 is the common denominator, we multiply EVERY TERM by 10 4y + 5y = 90 To multiply , we do 2y times 10 divided by 5, giving us 4yTo multiply , we do y times 10 divided by 2, giving us 5y 9y = 90 Adding the like terms 4y and 5y together gives us this equation "Undo" the 9 times y by dividing each side by 9 x = 10 This gives us the solution

Check by substituting 10 into the equation where we first cleared out the fractions

4 ( 10 ) + 5 ( 10 ) = 90

40 + 50 = 90

90 = 90