SOLUTION: For each of the figures, write Absolute Value equation in the form |x−c| =d, where c and d are some numbers, to satisfy the given solution set. x=-1/2, x=1/2

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Question 1155747: For each of the figures, write Absolute Value equation in the form
|x−c|
=d, where c and d are some numbers, to satisfy the given solution set.
x=-1/2, x=1/2

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
if the expression is positive, then the absolute value of the expression will be the expression.
if the expression is negative, then the absoolute value of the expression will be minus the expression.
when x = -1/2, abs(-1/2) = -1 * -1/2 = 1/2
when x = 1/2, abs(1/2) = 1/2
in both cases, abs(x) = 1/2
when you solve for x, you do the following:
if x is positive, then abs(x) = 1/2 becomes x = 1/2
when x is negative, then abs(x) = 1/2 becomes -x = 1/2
solve for x to get x = -1/2
what this says is that, when absw(x) = 1/2, then x = plus or minus 1/2.
in both cases, abs(x) will be equal to 1/2

here's a reference, one of several that can be found on the internet.

https://www.purplemath.com/modules/solveabs.htm

Answer by greenestamps(13332) (Show Source):
You can put this solution on YOUR website!

You want an absolute value equation in the form

that has the solution set x=1/2 and x=-1/2.

Interpret the equation as saying "the difference between x and c is d", allowing the difference to be either x-c or c-x. On a number line, this is equivalent to saying that x and c are separated by a distance d.

So for this particular problem, we are looking for numbers c and d for which both x=1/2 and x=-1/2 are the same distance d from c.

If x=1/2 and x=-1/2 are the same distance d from c, then c has to be halfway between x=1/2 and x=-1/2; and the distance d is the distance from that c to either of the x values.

Halfway between 1/2 and -1/2 is 0, so c is 0; and each of those x values is 1/2 unit from 0, so d is 1/2.

ANSWER:

It is easy to show that x=1/2 and x=-1/2 are the only two solutions to that equation.

Let's look at a more interesting example, with the two solutions being x=5 and x=13.

Halfway between 5 and 13 is 9; and the distance from 9 to either 5 or 13 is 4. So the equation is

That equation says the difference between x and 9 is 4; the two values for x are 9+4=13 and 9-4=5.

Or...

Solving that absolute value equation in the usual way, we have
or
or