Question

What nonnegative integers are solutions of the inequality | 2x - 1| <3 ? Show all work

Answer 1

Answer: 0 and 1

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Work Shown:

`|2x - 1| <3\\\\ -3 < 2x - 1 <3\\\\ -3+1 < 2x - 1+1 <3+1\\\\ -2 < 2x <4\\\\ -2/2 < 2x/2 <4/2\\\\ -1 < x < 2\\\\`

If x is a nonnegative integer, then writing -1 < x < 2 is the exact same as writing the roster notation {0, 1}. This is the solution set. We ignore anything negative and it must be a whole number smaller than 2.

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If we were to plug in x = 0, then we'd get a true statement

`|2x - 1| <3\\\\ |2*0 - 1| <3\\\\ |0 - 1| <3\\\\ |-1| <3\\\\ 1 <3\\\\`

I'll let you try out x = 1. That should result in a true statement as well.

Trying out x = 2 or larger will result in a false statement.

Answer 2

this is how i did it, hope it helps! :)