- #1
h00zah
- 16
- 0
how do you go about solving abs value inequalities with double variables when the abs value bars are on both the variables?
eg; |x| + or - |y| =, >, <, a
eg; |x| + or - |y| =, >, <, a
You don'th00zah said:but when |x| "is less than or equal to" a, how do you represent both rules at once?
Like this: -a <= x <= ah00zah said:I know that when |x| < a it must be -a < x < a, but when |x| "is less than or equal to" a, how do you represent both rules at once?
h00zah said:this is not h.w, we're doing this in class and we haven't been shown how to do this and there are no examples in my text.
An absolute value inequality is an inequality that contains the absolute value of a variable. This means that the variable can have a positive or negative value, but the absolute value ensures that the inequality is always true.
To solve an absolute value inequality, you must first isolate the absolute value expression on one side of the inequality. Then, you must consider the two possible cases: when the absolute value is positive and when it is negative. Finally, you must solve for the variable in each case and combine the solutions to find the final solution set.
The main difference between solving an absolute value equation and an absolute value inequality is the presence of inequality symbols. In an absolute value equation, the goal is to find the value(s) of the variable that make the equation true. In an absolute value inequality, the goal is to find the value(s) of the variable that make the inequality true.
Yes, absolute value inequalities can have more than one solution. This is because the absolute value function can produce two different values (positive and negative) for a given input. Therefore, when solving an absolute value inequality, there are typically two possible solutions.
Absolute value inequalities are important because they allow us to represent a range of possible values for a variable. This is useful in many real-world applications, such as determining possible temperature or distance values. Absolute value inequalities also provide a way to compare two quantities and determine which one is greater or less than the other.