Find a and b. If |x-3|<7, then a

Mathematics
- anonymous

Find a and b. If |x-3|<7, then a

Mathematics
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- anonymous

-7

- anonymous

If you were to substitute in -4 and10 in to a

- SnuggieLad

Are we doing piece wise functions here?

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## More answers

- anonymous

I do not understand? Piece wise functions?

- SnuggieLad

You haven't learned that? Then I got my answer.

- anonymous

LOL! Probably not, still in the beginning of College Algebra

- SnuggieLad

This is not college algebra.

- SnuggieLad

This is Algebra 2.

- anonymous

That makes senses, but it is called College Algebra at my school, and towards end of semester it gets in to Trig

- SnuggieLad

That is algebra two. And this is piece wise functions. I am going to go offline for a while be back in about ten or fifteen minutes.

- anonymous

Thank you

- jdoe0001

\(\bf |x-3|<7 \implies
\begin{cases}
+(x-3)<7\\ \quad \\
\bf -(x-3)<7
\end{cases}\)
if you were to solve those 2 cases, or scenarios, what would be the "values" of "x"?

- anonymous

I am so lost

- jdoe0001

hmm ok, what part?

- anonymous

When I work those problems, which I am probably not doing correctly I get:\[+(x−3)<7 = x<10\] \[−(x−3)<7 = x>4\] but the answer is -4, so I believe I am doing this wrong

- anonymous

So would I have multiplied both sides by -1 and then added three to both sides?

- jdoe0001

those answers are correct

- jdoe0001

now to make each of the inequalities look like " x + 4 "
just add 4 to each side :)

- jdoe0001

hmm... the 2nd one would be -4l

- jdoe0001

other than that, is ok... so \(\large {|x-3|<7 \implies
\begin{cases}
+(x-3)<7 \implies x < 10\\ \quad \\
-(x-3)<7 \implies x > -4
\end{cases}\\ \quad \\
x < 10 \implies x +4 < 14\\ \quad \\
x > -4 \implies x+4 > 0}\)

- jdoe0001

so you can see what "a" and "b" are

- anonymous

So I did end up with -4

- jdoe0001

\(\large {\begin{cases}
x < 10 \implies x +4 < 14\\ \quad \\
x > -4 \implies x+4 > 0
\end{cases}\implies \bf 0 < x +4 < 14}\)

- anonymous

So I would add 4 to both sides and not subtract?

- jdoe0001

well, they want \(\large x \color{red}{+}4\)
so you'd need to add, yes

- anonymous

-4

- jdoe0001

yeap
when yo have only left and right sides, you add/divide/multiply to BOTH sides
when you have left, middle, and right sides, you add/divide/multiply to ALL sides

- anonymous

-4

- anonymous

\[or we can say a \le 0,b \ge 14 .\]

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