SOLUTION: a+1/2 = 2a-1/5

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Question 1192117: a+1/2 = 2a-1/5
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
.

I don't know how to read it.


Is the left side   a + (1/2)   or   (a+1)/2 ?

Is the right side   2a - (1/5)   or   (2a-1)/5 ?


Use parentheses systematically and properly to avoid ambiguity.


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Comment from student : (a+1)/2 = (2a-1)/5.



My response. Ok, very good. 

Multiply both sides by 10 to run off the denominators.  You will get

    5(a+1) = 2*(2a-1).


Simplify step by step and find "a"

    5a + 5 = 4a - 2.

    5a - 4a = -2 - 5

       a    = -7.


ANSWER.  a = -7.


CHECK.  At a= -7, the left side of the original equation is  (a+1)/2 = (-7+1)/2 = -6/2 = -3.

                  the right side of the original equation is  (2a-1)/5 = (2*(-7)-1)/5 = -15/5 = -3.


                  It confirms that the answer is correct.

Solved.



Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

a+1/2 = 2a-1/5


5(a + 1) = 2(2a - 1) ------ Cross-multiplying

  5a + 5 = 4a - 2

 5a - 4a = - 2 - 5

      

You can do the CHECK!! 

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