Inequality and the Number Line

Label the number line with the solution set for |x-3| >= 2. Use the Mover buttons L(left) or R(right), to move the nearby item to the correct position on the graph. Use the RS(reset) button to move an item back to its initial position. When you have all of the items positioned, press the "Answer" button to see if you are right. Check your reasoning below.








Solution: Remove the absolute value signs and work with the two cases:
(a) +(x-3) >= 2, and (b) -(x-3) >= 2

Solving case (a):
x - 3 >= 2.
Use Rule 2 of inequalities to add 3 to each side to get
x - 3 + 3 = 2 + 3, or x >= 5.

Solving case (b):
-(x - 3) >= 2
Remove the parentheses to get
-x +3 >= 2
Use Rule 2 of inequalities to subtract 3 from eash side to get
-x + 3 - 3 >= 2 - 3, or -x >= -1.
Use Rule 5 of inequalities to multiply each side by -1 and change the
sense of the inequality:
-x *(-1) <= -1 * (-1), or x <= 1.