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ABSOLUTE VALUE IN REAL LIFE SITUATIONS. In real-world situations, we may choose to describe values using either negative numbers or the absolute values of those numbers, depending on the wording you are using. For example, if we have a balance of -$35 dollars in an account, we may also choose to represent that as a debt of $35. Solved Problems.
value of a number. The Absolute value of a number x is written |x| and is defined as |x| = x if x ≥ 0or|x| = −x if x<0. That is, |4| = 4 since 4 is positive, but |−2| = 2 since −2 is negative. We can also think of |x| geometrically as the distance of x from 0 on the number line. More generally, |x−a| can be thought of as the distance ...
When graphing integers on a number line, make sure to: Use at least 3 numbers. Use one number that is less then the number (to the left) and one number that is greater (to the right) Put a dot to indicate which integer you are graphing. Example: Graph -3 on a number line: -4. -3. -2.
An important property of the real numbers is that they are totally ordered, so we can compare any two real numbers, aand b, and make a statement of the form a bor b a, with strict inequality if a6=b. Given any two points on the real line, aand b, we call the set of points between aand ban interval.
Solving Absolute Value Equations Example: 13x + 12 (the absolute value is 'isolated' already) Steps: 1) Isolate Absolute Value 2) Solve for 'Positive Answer' 3) Solve for Negative Answer' 4) Check Solutions! (Plug into original equation) 'Positive" Answer. 'Negative" Answer. Check solutions: Example. 3X 12 3x 3X + 12 3(4) + 12 24 12 24 24 12 24 ...
No matter what is inside the absolute value symbols, the resulting number is always nonnegative. For example, j x2 + 3x 1j 0 for all real numbers x. The observations in the preceding paragraphs are summarized as two important properties of absolute value: Properties of Absolute Value For all real numbers x, jxj 0:
This lesson explains why a distance between two points, even if represented on a number line cannot be expressed as a negative number. Intuitively, the absolute value of a number may be thought of as the non-negative value of a number.
