Question

Which conjunction or disjunction is equivalent to the given absolute value inequality? Ix+5I < 18

a) x + 5 > 18 or x + 5 < - 18
b) x + 5 > 18 and x + 5 < -18
c) x + 5 < 18 or x + 5 >-18
d) x + 5 < 18 and x + 5 > -18

Answer 1

Just to be sure, you have notes right? I'm just asking, not judging.

Answer 2

The question says `which`

Do you have some options for us Jasmine? :)

Answer 3

Oh sure...I will post them right now :)

Answer 4

\[\Large\rm |x+5|\lt 18\]We can drop the absolute bars by putting a plus/minus sign,\[\Large\rm \pm(x+5)\lt 18\]So this is now really two equations:\[\Large\rm x+5\lt 18\]and\[\Large\rm -(x+5)\lt18\]The first equation is already in the form that we want.
For the second one, we'd like to move the negative to the other side so we're left with x+5 on the left.

Answer 5

So we'll divide the negative to the other side.
Do you remember what happens when you divide a negative across an inequality? :o

Answer 6

-18?

Answer 7

No no no :) Not just that, hehe

Answer 8

The inequality sign flips direction when we divide or multiply a negative across.

Answer 9

\[\Large\rm x+5\gt-18\]So yes, we get -18, but also the inequality changes directions, mm k?

Answer 10

oh yes! <?

Answer 11

So that narrows it down to C or D for us.

Answer 12

D