Interval notation problems???

Question

6: Write in interval notation: x < 5 AND x < 3

(-∞ , 3)

(-∞ , 5)

(3, 5)

(-∞ , ∞ )

7: Solve and write in interval notation: -2 ≤ x + 4 OR -1 + 3x > -8

(-∞ , ∞ )

[-6, -3)

[-6, -7/3)

[-6, ∞ )

8: Solve and write in interval notation: x − 3 ≤ 2 AND -x / 3 < 2

(- ∞ , -2/3)

(-∞, ∞)

(-6, 5]

(-6, ∞)

9: Solve and write in interval notation: -3x > 2 OR (2x + 2) / 3 > 0

(-2/3, 1)

(-1, -2/3)

(-∞, -2/3)

(-∞, ∞)

10: Solve and write in interval notation: -3 ≤ (x − 4) / 2 < 4

(-∞, ∞)

[-2, 12)

[1, 8)

(-2, Inf)

Answer 1

6. (-∞ , 3)  would be the answer because it MUST be less than 3, you would only go from -∞ to 3.  The parentheses means that it is non inclusive, make sure you understand that. Example: x Must be &gt; 4 and &lt; 6 you would do (4,6) but parentheses means that it doesn&#039;t include the 4 and 6.

7. Simplify each expression. -2 ≤ x + 4 would be -6 ≤ x (Subtract 4 from each side isolating x).  Kind of treat the greater than/less than signs as equal signs if you don&#039;t understand it. -1 + 3x &gt; -8 would be x &gt; (-7/3) (Add 1 to both sides and divide both sides by 3) and because it says OR instead of AND that means that it would be [-6, ∞ ).

8. Same concept as #7 but with AND. (-6, 5]

9. Same concept as #7&amp;8. (-1, -2/3)

10. Multiply the entire expression by 2, getting -6 ≤ x − 4 &lt; 8. And then add 4 to everything: -2 ≤ x &lt; 12. And your answer would be [-2, 12).

Hope that helped.