91Ó°ÊÓ

Modulus Function Formula

The value of the modulus function is always non-negative. If f(x) is a modulus function, then we have:

This means if the value of x is greater than or equal to 0, then the modulus function takes the actual value, but if x is less than 0 then the function takes minus of the actual value 'x'.

Absolute Value

Absolute value signs make the final result of the operations between them positive. When deciding on the order of operations, treat absolute value bars like parentheses.

|– 3| = 3: The absolute value bars make negative 3 positive.

| 3 | = 3: The absolute value bars leave positive 3 unchanged

– |– 3| = – 3: The absolute value bars make negative 3 positive. Then the negative sign takes effect, and the answer is a negative 3.

– | 3 | = – 3: The absolute value bars leave positive 3 unchanged. Then the negative sign takes effect, and the answer is a negative 3.

We know that: | 3 | = 3: The absolute value bars leave positive 3 unchanged

To solve the given expression – 10 +|x|,so that its value is greater than, the value ofx should be greater than or less than. Consider two cases:

Case 1: x is positive. The equation can be written as: $−10+x$

Since the numbers have an opposite sign, they will be subtracted and the sign of the greater number will be assigned to the answer.

The equation will yield a positive value greater than 0 when x has a value greater than.10 But if the value of x is equal to,10 the equation will yield.0

Assume x = 12 and the expression$−10+x$yields: $−10+12=2$ when x = 12 and 12 > 10 and the value of the expression$−10+x$greater than 0

Case 2: x is negative. The equation can be written as:$−10+|−x|$

Since,$|−x|\text{ â¶Ä‰}=\text{ â¶Ä‰}x$any negative value less than can be considered since an absolute value is used.

Assume x = – 15 and the expression$−10+x$yields: $−10+|−15|=−10+15=5$ when x = – 15 and – 15 < – 10 and the value of the expression$−10+x$greater than 0

We can write that if x has a positive value greater than 10 and if x has a negative value less than,$−10$the value of the expression$−10+x$greater than 0