Question

How do you solve `abs(x-3)> 5`?

Answer 1

x > 8 or x < -2

Explanation:

I x-3 I must be zero or positive

Consider I x - 3 I = 5

In this case x = 8 or x = -2

Now think about numbers either side of 8 and -2

If necessary substitute 7, 9 and -3 ,-1 into the original expression to see which side of 8 and -2 you need to be.

Answer 2

Solve |x - 3| > 5

Explanation:

Separate solving in 2 cases:

a. x - 3 > 5 -->`x > 8`

b. -(x - 3) = -x + 3 > 5 -> x < 3 - 5 -->`x < -2`

Graph:

==========|-2------|0-----------------|8=============