Absolute Value?

Question

If x = | 3 |, x = ________.
3, -3
3 only
-3 only
No solution


If x = | -2|, x = ________.
2 only
2, -2
-2 only
No solution


If | x | = 4, x = ________.
4, -4
No solution
4 only
-4 only


If | x | = 2/3, x = ________.
2/3 only
No solution
2/3, -2/3
-2/3 only


Solve for x: | x - 3 | = 4
7, -1
7 only
-7, 1
No solution


Solve for x: | x + 2 | = 8
6 only
-6, 10
No solution
6, -10

Answer 1

If Mod x = 3 that means x can have either +3 or -3 since the modulus (absolute) value is always positive.

Solve for x: | x - 3 | = 4
7, -1
7 only
-7, 1
No solution

Mod x - 3 = 4, so x - 3 = 4, or -4

If x - 3 = 4, x = 4 + 3 = 7

If x - 3 = - 4, x = -4 + 3 = -1

So, x will be 7 or -1

I hope you can do all others on this basis. Good luck.

Answer 2

The absolute value of something is essentially its 'length' or its 'size' - in other words you ignore any negative values.

so

|x| must always be positive for any x
and if |x| = y then x = +y or -y

The answers are:
3
2
4,-4
2/3, -2/3
7,-1 (x-3 = 4 or -4)
6,-10 (x+2 = 10 or -10)

Answer 3

The first one is 3, or -3
The second one is 2, -2
The third one is 4, -4
The fourth one is 2/3, or -2/3
The fifth one is 7 only
The sixth awnser is 6 only

Answer 4

Absolute value represents the distance from orgin. So if I am on 5 and you are on (-5) think, how far am i from zero? I am five units right.
Think, how far are you from zero, well since you're on (-5) that means you are five units from zero. right?
So, it has no reguard to the actual number you are standing on, but it does have to do with the distance from orgin (zero) you are.
Now go do your homework.....