# How do you solve abs(x-3)>=1?

Apr 3, 2018

$2 \ge q x \ge q 4$

#### Explanation:

From $| x - 3 | \ge q 1$ it follows that $x - 3 \le q - 1$ and $x - 3 \ge q 1$

Adding 3 to both sides of the equations we get
$x \le q 2$ and $x \ge q 4$ which are our two solutions.

Also, looking at the graph of $y = | x - 3 |$ we can see which values of y are greater than or equal to $1$ and these are indeed the values where x is less than or equal to 2, and where x is greater than or equal to 4.

graph{|x-3| [-10, 10, -5, 5]}