Question 1158602: Write the absolute value equations in the form
x−b
=c (where b is a number and c can be either number or an expression) that have the following solution sets:
All numbers such that x≥15.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
???!!
(1) "x-b=c" is not a form for an absolute value equation.
(2) Equations (either absolute value equations or any other kind) don't have solution sets like "all x greater than or equal to 15." They have one or more (or sometimes zero) discrete solutions.
Answer by ikleyn(52835)  (Show Source):
You can put this solution on YOUR website! .
It is just couple of weeks I observe your attempts to create a Math problem and/or to ask a Math question.
Since you do not use standard Math notations, and do not use a standard Math language, it is difficult
to understand the exact meaning of your request.
To define an absolute value equation, you should use the notation like this |x-a| = b.
It is a typical and a simplest equation with absolute value function in the left side.
Such form equation CAN NOT have that set of solutions x >= 15, as you requested.
In this sense the comment by the tutor @greenestamps is right.
Nevertheless, there are close forms of the absolute value equation,
that DO have this infinite continuous set of solutions x >= 15.
Such an equation is, for example, |x-15| - |x+15| = -30.
The Figure below shows the graph of the left side, making the solution EVIDENT.
The solution of equation |x-15| - |x+15| = -30. The left side function plot is shown in red.
The straight line y = -30 is shown in green.
It is VERY SHOCKING fact to see that an EQUATION may have infinite CONTINUOUS set of solutions.
But an ABSOLUTE VALUE EQUATION CAN (!).
Because it is highly non-linear equation.
When I got this idea and this solution, I was shocked.
I think, you will be shocked too, as well as @greenestamps !
Come again to this forum soon to learn something new (!)
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