[Suman Ganguli]

Post any WebWork questions from the 1st two sets here!

[Suman Ganguli]

example: post your question as a comment

“On Absolute Value Inequalities: Problem 6, I am not getting the correct solution for |x−20|≥ 93

I tried “(…, ….)”

[MohammadBelal]

I’m having trouble converting “x<−7 or 0≤x and x≠6” into interval notations, i attempted the problem 18 times and my original answer i put was “[0,inf)U(-inf,6)U(6,inf)”

[Samden Lama]

The answer you wrote as (inf and union), that is for the > or ≥ sign type of questions.
But if you have the < or ≤ signs, you dont need (inf and union). This is my way for memorizing.

Nvm to the previous reply, try this (-inf,-7)U[0,6)U(6,inf)

• This reply was modified 3 years, 7 months ago by Samden Lama.

[MohammadBelal]

Yeah it worked, Thanks.

[Suman Ganguli]

Glad it worked! Thanks for replying Samden.

I’ll add a little bit more explanation

if we just focus on the first two parts, “x<−7 or x <= 0”, then the solution is similar to the ones we found for abs value in inequalities–a union of two intervals which go off to infinity (one interval that goes off “to the left” to -inf, and the other that goes off “to the right” to +inf):

(-inf, -7) U [0, inf)

But now we need to “exclude” x=6 from the latter interval, to account for the “x≠6” clause. For that, we split up [0, inf) into two parts: the intervals 0 <= x < 6 and 6 < x. So we get:

(-inf, -7) U [0, 6) U (6, inf)