PeroK said:
anuttarasammyak said:
I think all you need to do is show one interval ##(a - \delta, a + \delta)##. You don't need all those different cases. The point ##x = 0## is not important here.kenny1999 said:
I guess that's ##0 < |x - a| < \delta##?kenny1999 said:
PeroK said:
No, "Another question" is really another, not related to the first question, yes the first question was ##0 < |x - a| < \delta##PeroK said:
You don't have to consider different values for ##a##.kenny1999 said:
It's ##x =a## that is excluded. I would just use ##(a-\delta, a)(a, a + \delta)## with round brackets to show the end points are excluded.kenny1999 said:
An absolute value inequality is an inequality that involves the absolute value of a variable, which is the distance of the variable from 0 on a number line. It can be represented as |x| < a or |x| > a, where a is a constant.
To represent an absolute value inequality with constants, you can use the symbols < and > to indicate less than or greater than, respectively. The absolute value of the variable should be placed between these symbols, and the constant should be placed outside the absolute value symbol. For example, |x| < 5 or |x| > 2.
The symbol < represents "less than", while the symbol > represents "greater than". In terms of absolute value inequalities, < is used when the inequality is less than a certain value, and > is used when the inequality is greater than a certain value.
Yes, an absolute value inequality can have more than one constant. For example, |x| < 3 or |x| > 2 and |x| < 5 are both valid absolute value inequalities with multiple constants.
To solve an absolute value inequality with constants, you can use the properties of absolute value to isolate the variable. If the inequality is |x| < a, the solution set will be all values of x that are within a distance of a from 0 on the number line. If the inequality is |x| > a, the solution set will be all values of x that are outside a distance of a from 0 on the number line.