Question

Y ≥ |x+2| + 5, solve in a graph

Answer 1

Y=-x+3 which is your answer

Answer 2

Answer: see the graph in the figure attached.

Explanation:


1) To solve graphically, draw the function |x + 2| + 5 and shade the region above the two lines.

You can see that graph in the figure attached.

2) You can figure out th is solution by solving the inequality in two parts.

i) First part, take x + 2 ≥  0

⇒ y ≥ x + 2 + 5 

⇒ y ≥ x + 7

Therefore, draw the line y = x + 7 and shade the region above the line.


ii) Second part, take x + 2 < 0 ⇒ | x + 2| = - x - 2

⇒ y ≥ - x - 2 + 5

⇒ y ≥ - x + 3

Therefore, draw the line y = - x + 3 and shade the region above the line.

4) The solution is the intersection of the two shaded regions, which is the one shown in the graph attached.