A. "Solve for w: (6w+1)/5≠2. Describe the solution in set notation."

Question

First I must find what number to substitute for "w" that WILL equal 2, correct? Then, determine the numbers that won't (I assume there will be far more of these)? What would be the most efficient way to go about this?

I'm also really struggling with this concept of writing equations that are always or almost always true. If I could receive some advice on how to tackle these sorts of problems, that would be helpful.

Thank you very much for the assistance. :-)

Take care!

Answer 1

You can solve it like almost any equation, but replacing the equality sign with \≠.

For example,
solve for q in (4a+3)/5≠3
so we can continue
4a+3≠5*3
4a≠15-3
4a≠12
a≠3 is the answer.
In set notation,
a ∈ R\3, or
a ∈ (-∞,3)∪(3,∞)
(Remember: this is an example)