Question 68769
9x-3<6-x+9x 
What do you do after combining like terms?


That depends upon the specific equation, inequality or expression. Combining like terms is frequently only one of several steps  that leads toward solving the problem or simplifying the expression.  Thes steps include but are not limited to collecting like terms, adding the same quantity to both sides of the equation, subtracting the same quantity from both sides of the equation, multiplying both sides by the same quantity and dividing both sides by the same quantity providing the quantity that you are dividing by is not zero. In fact, sometimes it's necessary to collect like terms multiple times.  In order to solve for an unknown, you will normally need to get the knowns together and the unknowns together, preferably on different sides of the equal or inequality sign. Lets use you problem as an example:

{{{9x-3<6-x+9x}}} 

We can see by inspection that on the right side of the inequality we can combine some like terms, namely -x+9x which equals +8x.  Now we have:

{{{9x-3<6+8x}}} 

Now let's subtract 8x from both sides and also add 3 to both sides and we get:

{{{9x-8x-3+3<6+3+8x-8x}}}

Now we collect like terms AGAIN!!!! and we have

{{{x<9}}}


Hope this helps------ptaylor