SOLUTION: I have the following question that I don't really get how to do. It is as follows: "Solve the following inequality problems. You must give your answer using the interval notatio

Question 855763: I have the following question that I don't really get how to do. It is as follows:
"Solve the following inequality problems. You must give your answer using the
interval notation. You must also give you answer in graphical form (using the
number line).
(a) 7 - 5x < -3 or 2x - 1 ≤ x - 2.
(b) 2 - 3x < 8 and 4x - 2 ≤ 3x + 1.
Can someone please answer the question so that I can understand how it's done?
Thank you in advance :)
zeedee
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(a) 7 - 5x < -3 or 2x - 1 ≤ x - 2
7 - 5x < -3
-5x < -10
when multiplying or dividing by a negative reverse the < or >
x > 10
2x - 1 ≤ x - 2
x ≤ -1
so x is ≤ -1 or > 10
there are two intervals to mark on the number line
(negative infinity, -1] this is closed on the right because -1 is included
(10, infinity)
(b) 2 - 3x < 8 and 4x - 2 ≤ 3x + 1
2 - 3x < 8
-3x < 6
x > -6
4x - 2 ≤ 3x + 1
x ≤ 3
so x > -6 and ≤ 3
we have one interval which is closed on the right
(-6, 3]

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