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The range of all real numbers x such that 2x − 5 < 7 OR 4x + 10 > 6 is___
a. (-1,6)
b. (-infinity, infinity)
c. an empty set
d. (6,-1)

Respuesta :

Noah11012
First, simplify the two inequalities.

2x - 5 < 7
2x < 12 <-- Add 5 to each side
x < 6 <-- Divide both sides by 2

4x + 10 > 6
4x > -4 <-- Subtract both sides by 10
x > -1 <-- Divide both sides 4

Now we have the compound inequality x < 6 OR x > -1

To fulfill the first inequality, x has to be less 6. For the second inequality, x has to bigger than -1.

So, the answer is B. (-infinity, infinity).

The range of all real numbers x such that [tex]2x -5 < 7[/tex] OR [tex]4x + 10 > 6[/tex] is  (-infinity, infinity)

What is range?

The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number.

According to question, we have to find the the range of all real numbers x such that [tex]2x -5 < 7[/tex] OR [tex]4x + 10 > 6[/tex]

Now, [tex]2x -5 < 7[/tex]

      ⇒[tex]x < 6[/tex]

Also, [tex]4x + 10 > 6[/tex]

      ⇒[tex]x > -1[/tex]

From both equation [tex]x[/tex] belongs to (-infinity, infinity)

Hence, Option(B) is correct.

Learn more about range here:

https://brainly.com/question/12777994?referrer=searchResults

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