Question

Find the solutions of the inequality.
| x - 5 | ≥ 3

Answer 1

\[|f(x)| \ge 3 => f(x) \ge 3 \text{ or } f(x) \le -3 \]

Think about it :

Say we call this line f(x)

-----|-----------|--------
-3 3
We want the distance to be greater than 3
That means we want f(x) to be
******] [**********

Answer 2

Since f(x)=x-5
we have
\[x-5 \ge 3 \text{ or } x-5 \le -3 \]
You need to solve both of these inequalities for x

Answer 3

first you set up both equation
x-5≥ 3
x-5≥ -3

Answer 4

then you bring over the 5 to the 3 and -3
so +5 and +5

Answer 5

I believe this will help you understand