Precal, Inequalities involving absolute value

In summary, absolute value is a mathematical concept that represents the distance of a number from zero on the number line. To solve inequalities involving absolute value, you need to isolate the absolute value expression and consider two cases. The difference between absolute value and regular value is that absolute value is always positive and represents distance, while regular value can be positive, negative, or zero and is the actual value of a number. To graph absolute value inequalities, you need to rewrite the inequality in a specific form and then plot the vertex and use the slope to determine the direction of the graph. Absolute value and inequalities have various applications in fields such as engineering, physics, and economics.
  • #1
name_ask17
146
0

Homework Statement



DIRECTIONS: Express the intercal in terms of an inequality involving absolute value.
PROBLEM: (-4, 4)
MY STEPS:
1: (-4, 4)
2: -4<x<4
3: |x|< 4 MY ANSWER
Is that correct? Is step 3 correct? The only reason that I included that part is becuase it says "Involving absolute value," but I am not sure if that is what the question is really asking. Please advise if you can. Thank you in advance.
 
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  • #2
hi name_ask17! :wink:

yes, that's fine :smile:

(and step 3 is obvious from step 1, you don't need step 2)​
 
  • #3
lol. thanks tiny tim!
 

FAQ: Precal, Inequalities involving absolute value

1. What is the definition of absolute value?

Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. It is always positive and is denoted by two vertical lines surrounding the number.

2. How do you solve inequalities involving absolute value?

To solve inequalities involving absolute value, you need to isolate the absolute value expression on one side of the inequality and then consider two cases: when the expression inside the absolute value is positive and when it is negative. For each case, you can remove the absolute value by changing it to a positive or negative version of the expression and then solve for the variable.

3. What is the difference between absolute value and regular value?

Absolute value always gives a positive number, while regular value can be positive, negative, or zero. Absolute value also represents distance, while regular value is the actual value of a number.

4. How do you graph absolute value inequalities?

To graph absolute value inequalities, you first need to rewrite the inequality in the form of y = |ax + b| + c, where a, b, and c are constants. Then, you can plot the vertex at (b, c) and use the slope of a to determine the direction of the graph. Finally, you can shade the appropriate region based on the inequality symbol.

5. What are some applications of absolute value and inequalities?

Absolute value and inequalities are used in a variety of fields, such as engineering, physics, and economics. In engineering, they are used to calculate distances and determine the strength of materials. In physics, they are used to describe the motion of objects. In economics, they are used to represent supply and demand, as well as inequalities in income distribution.

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