Question

Which conjunction or disjunction is equivalent to the given absolute value inequality?

|x + 5| > 18
I got this am I right or wrong?
x + 5 > or x + 5 < -18

Which is the solution set to the given inequality?
|x + 3| < 12
I got -15 u 9 am i right or wrong?



HELP PLZ!

Answer 1

\[\left[\begin{matrix}x>-2 & \\ x+y<4& \end{matrix}\right]\]
NEED HELP ON THIS ONE TO

Answer 2

|x + 5| > 18 implies x + 5 > 18 OR x + 5 < -18

Answer 3

x + 5 > 18
x > 13
OR
x + 5 < -18
x < -23

\(x = (-\infty, -23) \cup (13, \infty)\)

Answer 4

|x + 3| < 12 implies x + 3 < 12 AND x + 3 > -12
x + 3 < 12
x < 9
AND
x + 3 > -12
x > -15

Solution: -15 < x < 9
In interval notation: (-15, 9).

Answer 5

would it be written like this? @aum

Answer 6

wouldnt it be [-15,9]

Answer 7

No, the end points -15 and 9 are not included in the solution -15 < x < 9 and so it should be (-15,9).

If the solution had been \(-15 \le x \le 9\) then the solution would be [-15. 9] where both end points are included in the solution.

So for this problem the solution is: (-15, 9).

Answer 8

oh I see thanks!!!! can you help me on this last one plz
\[\left[\begin{matrix}y >-2 & \\ x+y<4& \end{matrix}\right]\]