Question

2. Solve and graph.

(a) Write the inequality as two inequalities without absolute value.
(b) Solve the inequality and write the solution set.
(c) Graph the solution on a number line.

Answer 1

|x - 2| > 5

if x >= 2
x - 2 > 5
x > 7

if x < 2
-x + 2 > 5
x < -3

hence the solution is: x belongs to (-inf, -3)U(7, inf)

graphical representation of solution
---------------------------) (--------------------
-inf -3 7 inf