Question

How many solutions are there for the equation? |x-4| = 9 a) one solution b) two solutions c) no solution

Answer 1

You have |x-4| = 9. There will be two solutions to the equation and here's how to solve them.

|x-4| = 9

x-4 = 9

x = 13

|x-4| = -9

x-4 = -9

x = -5

So the two solutions of these variables are 13 and -5. Try them in the equation and it'll work.

Answer 2

Remark.

The very easiest way to do this task is to graph it.

The key point to understand is that there is no intercept point along the x axis. The correct answer is that there are no solutions.

Notice the vertex. That is the key fact. The y value is 9 units above the x axis which is just what the equation is telling you. Also the x value is 4 units to the right.