Question

Which statement is equivalent to |x – 19| < 7
1)x – 19 < 7
2)x – 19 < -7
3)x – 19 < 7 or x – 19 > -7
4)-7 < x – 19 < 7

Answer 1

4.

Answer 2

4.

Answer 3

thankyou!

Answer 4

Remember that if |x|<k, then x < k or -x < k, which simplifies into x > -k. These two combine into -k < x < k

So that means that |x-19|<7 turns into

x-19 < 7 and x-19 > -7

and these two combine into

-7 < x-19 < 7