SOLUTION: Write an absolute value equation that has the solutions x=8 x=8 and x=18

Question 1122941: Write an absolute value equation that has the solutions
x=8
x=8
and
x=18
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The absolute value equation means that b is the difference between the unknown number x and the fixed value a.

For example, means the difference between x and 7 is 3. On a number line, that means the two solutions to the equation are the two numbers that are a distance 3, in either direction, from 7. Those two numbers are 7-3=4 and 7+3=10.

In that example, the distance between the two solutions is 6, because they are 3 in opposite directions from 7.

So if you know the two solutions to an absolute value equation, you know the difference between them. Then you know that the "a" in the equation is halfway between the two solutions; and then you know the "b" in the equation is the distance from a to either solution.

Here is an example; you can use it to figure out the answer to your question.

Write an absolute value equations with the solutions x = -2 and x = 18.

The difference between the two solutions is 18-(-2) = 18+2 = 20. Half that difference is 10; and 18-10 = 8. So the "a" in the absolute value equation is 8, and the "b" is 10. So

We can check that answer by finding the two numbers that are a distance of 10 from 8; those two numbers are 8-10 = -2 and 8+10 = 18.

Now use that same process for your example.

(1) what is the difference between the two solutions?
(2) what is the number halfway between the two solutions; and how far is it from that number to each of the two solution?
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