How do you solve #27- 11x = x - 33#?

1 Answer
Apr 11, 2018

#x=5#

Explanation:

#27-11x=x-33#

You want the answer to be of the form #x=?#

So, start by "undoing" the part of the equation furthest away from the variable: in this case, #+27# and #-33# are furthest away from the #x# on both sides

1. For this explanation, we will "undo" the #-33# on both sides

#27-11x+33=x-33+33#

2. Then collect like terms

#27+33-11x=x#

#60-11x=x#

It should be noted that it is possible to start by "undoing" the #+27# in a similar way

Now we want to have all the #x#'s on one side so that it can be of the form #x=?#

3. "Undo" the #-11x# on both sides

#60-11x+11x=x+11x#

4. Collect like terms

#60=12x#

To "solve" the equation the answer must be a "singular" #x=?#

5. "Undo" the #12*x# on both sides

#60/12=(12x)/12#

6. Collect like terms and cancel appropriately

#5=x#

Therefore

#x=5#

=================================================

*Footnote*

In this context, "undo" means to "do the opposite of", so to "undo" a #-2# it is necessary to #+2#. However, this must be done on both sides of the equation in order to maintain its balance.

Eg: if 1kg was to be added to one side of a balance scale, the same weight must be added to the other side so that the balance is maintained.