MAT 104 Quiz 4
Wednesday, September 15, 2004
1. Solve the inequality below and write your answer in set builder notation.
(x−3) <−2(x+ 2) ≤x
Split this compound inequality into the two inequalities
x−3<−2(x+ 2) and −2(x+ 2) ≤x
The first inequality is
x−3<−2(x+ 2) ⇐⇒ x−3<−2x−4
⇐⇒ 3x < −1
⇐⇒ x < −1
3
and the second inequality is
−2(x+ 2) ≤x⇐⇒ −2x−4≤x
⇐⇒ −4≤3x
⇐⇒ −4
3≤x
⇐⇒ x≥ −4
3
In set builder notation, the solution set is
½x| −4
3≤x < −1
3¾
2. Write your answer in interval notation.
·−4
3,−1
3¶
3. Indicate your solution on the number line below.
0-1-2-2-4-5 1 2 3 4 5