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Solving Equations with Fractions

by Debra

Please help to solve this equation with fractions:

-5= -19- x/7

Karin from Algebra Class says:

Whenever you have a fraction within an equation, you can always eliminate that fraction by multiplying all terms by the denominator. If you have more than one fraction, then you would multiply by the least common denominator.

Step 1: Multiply all terms by 7 to get rid of the fraction.

(7)-5 = 7(-19 - x/7)

-35 = -133 - x When you multiply 7 (x/7) the 7 in the numerator and the 7 in the denominator simplify to 1 (or you could say they cancel out). Therefore, you are left with what was in the numerator.

So, now we have:
-35 = -133 - x

Step 2: Add 133 to both sides.

-35 + 133 = -133 + 133 - x

98 = -x

Step 3: Since x is negative, we can multiply all terms by -1, to make x positive.

(-1) 98 = -x(-1)

-98 = x

Your final answer is x = -98.

Then you can check by substituting:

-5 = -19 - (-98/7)
-5 = -5

I hope this helps. You can also review the lesson on solving equations with fractions on the following web page.


Best of luck,

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