SOLUTION: Good Evening: The problem is a simple one, however my teacher is showing a method to clear out the decimals before solving. The problem is: (x-17.7)+19.6= 27.8 My teacher

Algebra ->  Equations -> SOLUTION: Good Evening: The problem is a simple one, however my teacher is showing a method to clear out the decimals before solving. The problem is: (x-17.7)+19.6= 27.8 My teacher      Log On


   

Question 542330: Good Evening:
The problem is a simple one, however my teacher is showing a method to clear out the decimals before solving. The problem is:
(x-17.7)+19.6= 27.8
My teacher advised me to multiply both sides by 10. I am confused. Could please help me solve this equation
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

Yes, multiplying both sides of the equation will make this MUCH easier to work with (in theory):

%28x-17.7%29%2B19.6=27.8

x-17.7%2B19.6=27.8

Now multiply both sides of the equation by 10 (by multiplying EACH term by 10).

10%2Ax-10%2A17.7%2B10%2A19.6=10%2A27.8

10x-177%2B196=278

Looks a bit simpler to solve, doesn't it?

Now solve the equation as normal:

10x-177%2B196=278

10x%2B19=278

10x=259

x=259%2F10

x=25.9

You would get the same answer if you DIDN'T clear out the decimals by multiplying both sides of the equation by 10.

In some cases it can be really helpful, not really all that much in this case.

You can also use a similar method to clear out fractions by multiplying both sides of the equation (each term) by the Least Common Denominator of the fractions.

I hope this helps!