Respuesta :

luisejr77

Answer:

[tex]-1.8<x<-1[/tex]   (In Interval Notation: [tex](-1.8,-1)[/tex] )

Step-by-step explanation:

Given the following binomial:

[tex]5x+3[/tex]

You know that if this binomial is in the interval:

 [tex](-6, -2)[/tex]

It must be:

[tex]-6<5x+3<-2[/tex]

Therefore, in order to find for what values of "x" the binomial  [tex]5x+3[/tex] belongs to the given interval, you need to solve the inequality.

Then, you get:

[tex]-6<5x+3<-2\\\\-6-3<5x<-2-3\\\\-9<5x<-5\\\\\frac{-9}{5}<x<\frac{-5}{5}\\\\-1.8<x<-1[/tex]

Now, you can write this in Interval notation.

Since it is an Open Interval, you must use parentheses. Then, this is:

[tex](-1.8,-1)[/tex]

adioabiola

The values of x for which the binomial 5x+3 belongs to the interval (−6; −2) is given as;

(-1.8; -1)

According to the question, the binomial function 5x + 3 belongs to the interval (-6; -2).

In essence the values of the function lies between -6 and -2.

Mathematically; we have;

  • -6 < 5x + 3 < -2

  • -6 -3 < 5x < -2 -3

  • -9/5 < x < -1

The values of x for which the binomial 5x + 3 belongs to the interval (-6; -2) is given as an inequality;

  • -9/5 < x < -5/5

OR

  • -1.8 < x < -1

Put differently, this can be written as;

(-1.8; -1)

Read more;

https://brainly.com/question/23956343

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