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erma4kov [3.2K]
3 years ago
14

Solution to the compound inequality –6 ≤ 2 + 6 ≤ 6 -12≤x≤0 6≤x≤6 -6≤x≤0 0≤x≤6

Mathematics
1 answer:
Ket [755]3 years ago
5 0
-6 < = 2x + 6 < = 6....subtract 6 from all sections
-6 - 6 < = 2x + 6 - 6 < = 6 - 6...simplify
-12 < = 2x < = 0...divide all sections by 2
-12/2 < = (2/2)x < = 0/2....simplify
-6 < = x < = 0...by the way, I cant put the line under the inequality sign to show the equal sign...so I just put the = sign with the inequality sign
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Write the set of points from −2 to 6 but excluding 3 and 6 as a union of intervals:
KengaRu [80]

Answer:

[-2,6] - {3} - {6}  =   [-2,3)  ∪   (3,6)

Step-by-step explanation:

Union Of Intervals

Let us assume two interval A =  (a,b) and  C = (c,d).

Their union is written as :   A ∪ C = (a,b) ∪ (c,d)

Now, if interval is written in form [a,b] ⇒  a and b are INCLUDED in interval

Also, if interval is written in form (a,b) ⇒  a and b are NOT INCLUDED in interval

Here, the given interval is [-2,6]

excluding 3 and 6 from this will give:

[-2,3)  ∪   (3,6)

The first set is [-2.3)   where  -2 is INCLUDED but 3 is NOT INCLUDED.

The second set is (3,6)   where 3 and 6 both are  NOT INCLUDED.

Hence,   [-2,6] - {3} - {6}  =   [-2,3)  ∪   (3,6)

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