Trying to help daughter with algebra?

Question

problem: using least common denominator: 20-x/3=x/2

How do we do this?

Answer 1

You have x/3 and x/2 and the LCD is 6 so u multiply x/3 to 2x/6 and x/2 to 3x/6 and u get: 20 - 2x/6= 3x/6. You switch sides (not forgetting to change the sign) and u get 20= 3x/6 + 2x/6; 20= 5x/6. U multiply the whole equation by 6 and u get 120 = 5x therefore x=120/5=24. Good day!  

Answer 2

First you need to collect all the  x-terms together on one side of the equation (and when you swap sides, you change the sign from plus to minus,  or from minus to plus)

So  20 - (x / 3)  =  x / 2  becomes  20  =  (x / 2)  + (x / 3)

(And you should use plenty of brackets to keep separate terms which need to be kept separate.  In your statement of the question, for example, it is not exactly certain that you do not mean  (20 - x)/3 = x/2, which is a different problem.)

It is more conventional to put the x-terms on the left, so let's re-write it as

(x / 2)  +  (x / 3)  =  20

Add the two parts on the left hand side as you do normally for fractions:  common denominator is  2 x 3 = 6, so we get

(3x  +  2x) / 6  =  20

Now we can remove the fraction by multiplying both sides by 6 :

3x + 2x  =  6 x 20,  or  5x  =  120

Now get x on its own by dividing both sides by 5 :

x  =  120 / 5  =  24

And finally, check that the answer satisfies the original equation by substituting  24 for x :

20  -  (24 / 3)  =  20 - 8  =  12

and  24 / 2  =  12

Which confirms that  the solution is indeed  x = 24.