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Angelina_Jolie [31]
2 years ago
10

Find the values of x for which the following inequalities are satisfied 2x^2+3x<14

Mathematics
1 answer:
deff fn [24]2 years ago
6 0

Answer:

x<-3.5 or x<2

Step-by-step explanation:

2x²+3x<14

2x²+3x-14<0

2x²-4x+7x-14<0

2x(x-2)+7(x-2)<0

(2x+7)(x-2)<0

2x+7<0 or x-2<0

2x<-7 or x<2

x<-3.5

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<h3>Answer: Choice B</h3>

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Explanation:

The given set is in roster notation. Think of a baseball or football team (or any sports team) how their roster lists out all of the players. In this case, each number is like a player.

The idea here is to simplify the set so we don't have to write out every single item. Instead we have a rule to make things a bit simpler.

In this case, the set {7, 8, 9, 10, 11, 12, 13, 14} describes all natural numbers from 7 to 14

This means we can say {x | x is a natural number with 6 < x < 15}

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An equivalent set would be \{ x | \text{ x is a natural number with } \ 7 \le x \le 14\} and here we have "or equal to" involved. For this example, the endpoints x = 7 and x = 14 are included.

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Something like choice A and choice D are not complete answers because we don't know if x is a whole number, natural number, rational number, real number, etc. If x was say a real number, then x = 10.75 would be involved with choice A. But 10.75 is not part of the original set.

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