# How do you graph and solve  |x – 2| <=3?

Feb 10, 2017

$x \in \left[- 1 , 5\right]$. The section (segment ) of the x-axis of the shaded region in the graph is the graph, for this solution

#### Explanation:

graph{y-|x-2|+3>=0 [-7.2, 7.1, -3.56, 3.597]}

Algebraically,

$x - 2 \le 3$ giving $x \le 5$, when x >=2 and#

$- \left(x - 2\right) \le 3$ giving $x \ge - 15$, when x <=2

Graphically, this interval $x \in \left[- 1 , 5\right]$ is the subset y = 0 of the set

for $y \ge | x - 2 | - 3$, in the Socratic graph.