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15: Solve the inequality for x and use interval notation: 2x – 3 > 5
(-∞ , 4)
(-∞ , 4]
[4, ∞ )
(4, ∞ )


16: Solve the inequality for x and use interval notation: -4 + x < -3 – 2x
(-∞ , (1/3))
(-∞ , (1/3)]
[(1/3), ∞ )
((1/3), ∞ )


17: Solve the inequality for x and use interval notation: (2/3)x – (4/3) ≥ (1/4)
(-∞ , (19/8))
(-∞ , (19/8)]
[(19/8), ∞ )
((19/8), ∞ )

2007-02-20 01:40:08 · 2 answers · asked by me1026 1 in Education & Reference Homework Help

2 answers

15. 2x - 3 > 5
2x > 8
x > 4 What this says is that x is greater than 4. So the solution set would be all x that is greater than 4. So (4,Infinity). You use parenthesis because there is no = sign (such as >=) which means that the number 4 itself does not satisfy the inequality.

16. -4 + x < -3 - 2x
3x < 1
x < 1/3
Using the same logic as above, (-Infinity, 1/3)

17. 2/3 x - 4/3 >= 1/4
2x - 4 >= 3/4 Multiplied by 3
2x >= 19/4
x >= 19/8
Since there is an equal sign, 19/8 can be in the solution set. So [19/8, infinity)

2007-02-20 02:11:50 · answer #1 · answered by Fresh 2 · 1 0

16: Solve the inequality for x and use interval notation:
-4 + x < -3 – 2x
-4 + 3 < -2x - x
-1< -3x
(1/3) > x
x < (1/3)
Since, x < (1/3), the solution interval is (-∞ , (1/3)).
[Note: if x ≤ (1/3), then the answer would be (-∞ , (1/3)]. This notation includes (1/3) in the solution interval.]

2007-02-20 02:15:41 · answer #2 · answered by S. B. 6 · 0 0

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