what is the absolute value of x-5,if xis less than 5?
Answers
Step-by-step explanation:
Absolute value of x = 4. Ans.
Answer:
Absolute Value Symbol
To show we want the absolute value we put "|" marks either side (called "bars"), like these examples:
|−5| = 5 |7| = 7
vertical bar The "|" can be found just above the enter key on most keyboards.
More Formal
More formally we have:
Absolute Value
Which says the absolute value of x equals:
x when x is greater than zero
0 when x equals 0
−x when x is less than zero (this "flips" the number back to positive)
So when a number is positive or zero we leave it alone, when it is negative we change it to positive using −x.
Example: what is |−17| ?
Well, it is less than zero, so we need to calculate "−x":
− ( −17 ) = +17
(Because two minuses make a plus)
Useful Properties
Here are some properties of absolute values that can be useful:
|a| ≥ 0 always!
That makes sense ... |a| can never be less than zero.
|a| = √(a2)
Squaring a makes it positive or zero (for a as a Real Number). Then taking the square root will "undo" the squaring, but leave it positive or zero.
|a × b| = |a| × |b|
Means these are the same:
the absolute value of (a times b), and
(the absolute value of a) times (the absolute value of b)
Which can also be useful when solving
|u| = a is the same as u = ±a and vice versa
Which is often the key to solving most absolute value questions.
Example: Solve |x+2| = 5
Using "|u| = a is the same as u = ±a":
this: |x+2| = 5
is the same as this: x+2 = ±5
Which has two solutions:
x+2 = −5 x+2 = +5
x = −7 x = 3
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