Question

What does the inequality |x + 5| > 3 equal?
(I don't understand why it isn't -8 13 years ago

Answer 1

suppose x is positive, then for any value of x, the inequality will hold true,,, so dis implies that x>=0 is a solution

Answer 2

now let us talk when x is negative, clearly, x>-2 will satisfy(since we want the magnitute of the value inside mod to be greater then 3)
so this implies x>-2 will always satisfy( by combining our first nd second result)

Answer 3

now all the values btw -8 nd -2 wont satisfy( again keep magnitute concept in mind),,, so it implies x>-2 nd x<-8 satisfies so its d aswer

Answer 4

mode means it can also be positive and -ve

Answer 5

there fore you get two answers

Answer 6

ya mode is over the complete term x+5, so we can take x to be negative or positive nd likewise will get two answers(as shown above)

Answer 7

Well let's see what the following expression means:
| f(x) | < k
The absolute value of f(x) is less than k
Now, absolute value of a positive quantity is the quantity itself while absolute value of a negative quantity is negative of that.
For example, | -5 | = -(-5) = 5
So if | f(x) | < k,
this means that f(x) can lie between -k and k
i.e.
-k < f(x) < k

Similarly, let's see what | f(x) | > k means
if f(x) is positive then f(x) must be > k
if f(x) is negative then f(x) must be < -k (ex: if k = 5 then | -5.1 | = 5.1 > 5)
Thus f(x) > k and f(x) < -k

Coming to the question at hand now,
we have | x+5 | > 3
=> either x+5 > 3 or x+5 < -3
=> x+5-5 > 3-5 or x+5-5 < -3-5
=> x > -2 or x < -8