how to solve equations with fraction

Question

-2/5[10x-25]=8x+4

 

Answer 1

Hello,

 

In order to solve this equation and many like it we will first need to know and use PEMDAS (parenthesis, exponents, multiplication/division - from left to right, addition/subtraction -  from left to right). 

 

Step one:

First distribute the fraction -2/5 to everything on the inside of the parenthesis. This means that you will multiply (-2/5)( 10x) which will equal -4x   and then multiply (-2/5)(-25) which will equal 10.   So now on the left side of the equal sign you will have    -4x + 10 set equal to the original right side.

 

You should have   -4x + 10 = 8x - 4

 

Now it is your decision to move all of the terms with variable either to the left OR right of the equal sign. I am left handed so let's just move all the Xs to the left side.  In order to do this I need to locate the like terms: -4x  and 8x.  Since I am deciding to move all the variable to the left, this means that I have to move all the regular number (without variables next to them to the right)

 

-4x  +  10  =  8x  - 4

 

Step two: combine like terms by performing the opposite operation on both sides of the equal sign

 

-4x + 10 = 8x  - 4

 

-8x            -8x        The opposite of 8x which is -8x on both sides of the equal sign. 8x -8x = 0 

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-12x  + 10 = 0 - 4       - - - - - - >       -12x + 10 = 4

 

Step three: solve for the remaining variable. In this case the variable is x. This is a multi step equation.  *remember how I said we were to move all the variable to the left, now its time to move all the constants (numbers without variables) to the right

 

 

-12x + 10 =  4

 

         -10      -10    The opposite of 10 which is -10 on both sides of the equal sign. 10 -10 = 0

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-12x + 0 = -6      - - - - - - >    -12x = -6

 

Now is the last step. I am still doing opposites to solve. -12x is the same thing as saying -12 times x. The opposite of times (aka multiplication) is division. So my final step is to divide by -12 on both sides in order to finally solve for x.

 

 

-12x  =  -6

-----       -----         -12 / -12 is 1. So in essence we now have 1x on the left side of the equal sign

-12         -12   

 

 

x = -6/-12 or 6/12 or 1/2            

 

 

There are other methods to solving this problem, however I find this one the best.

I hope this helps :-)