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Solving Basic Guys

Try sticking some numbers in!

                                              2x - 5 is greater than or equal to 7

when x = 6, 2(6) - 5 is greater than or equal to 7 which gives 7 is greater than or equal to 7. Yep-that's true!

when x = 10, 2(10) - 5 is greater than or equal to 7 which gives 15 is greater than or equal to 7. Yep-that's true!

What about something less than 6?

     when x = 2, 2(2) - 5 is greater than or equal to 7 which gives -1 is greater than or equal to 7. false!

So, any number that is 6 or bigger works in the inequality.

In interval notation, our answer is

[ 6 , infinity )

Here's another one:

3x + 2 < x - 4

Pretend it's  3x + 2 = x - 4  and go for it!

 3x + 2 < x - 4, ditch the smaller x guy by subtracting x from both sides which gives 2x + 2 < -4, ditch the 2 by subtracting 2 from both sides which gives 2x < -6, ditch the 2 by dividing both sides by 2 which gives x < -3