Absolute equations and inequalities??? Help!

[donfcai]

Solve when 0<a<1

ax>[x-a]

Not sure how to describe this equation, have tried to find similar examples on line, but to no avail.

Thanks for any help to get me started.

 

[mmm4444bot]

(Another "lock-up" while editing; Microsoft products sure waste a lot of my personal time. :x )

Hi there:

At these bulletin boards, volunteers are here to guide people through their specific issues. So, we like to get as much information as possible up front.

Also, we can type absolute value symbols, using a standard keyboard. (Shifted backslash, on many keyboards.) Square brackets have a different meaning.

Rather than searching for finished exercises that match the form of this one, a better approach is to use what you've already learned about inequalities and absolute value.

(I claim that mindless substitution of numbers and symbols into corresponding patterns from finished exercises leads neither to enlightenment nor exam preparation. :idea: )

ax > |x - a|

You made no statements about what you already know, so you've forced me to assume the following.

(1) You understand the definition of absolute value

(2) You understand the rules involved when solving inequalities.

In order to get rid of the absolute value symbols, we need to consider cases.

Clearly, we need to know when the expression x - a is either positive or negative.

CASE x > a: in this case, the expression x - a is positive, and the inequality becomes:

ax > x - a

Solve this in the usual way.

CASE x < a: in this case, the expression x - a is negative, and the inequality becomes:

ax > a - x

Solve this in the usual way.

CASE x = a: this case says that x - a is zero, and the inequality becomes trivial:

x^2 > 0

This is always true, since x cannot be zero, in this case.

So, solve the first two cases, and interpret the results.

If you need more help, then please show whatever work you can or at least explain what you're thinking, so that we can determine where to continue helping you.

When seeking help, the more information that you provide about your situation up front, the sooner and better the responses you'll get. Without information, it's hard to know where to start, and time is probably wasted for everybody involved.

Cheers ~ Mark

 

[donfcai]

Mark

Thanks for help, however, had to go to next class before I got your inputs. Got futher inputs from instructor.

Thanks again for help.