An airline company does not charge an extra fee if the weight of a passenger's luggage is less than 55 pounds. Part A
On the number line, represent the values when the airline company does not charge an extra fee.

Part B
Create an inequality that represents this situation. Let p represent the weight of a passenger's luggage

Let's solve first the part B.

We know that the company does not charge an extra fee is the luggage is less than 55 pounds.

Then if p represents the weight of the passenger's luggage, we need to have:

p is smaller than 55 lb

We also can write this as:

p < 55lb

where the symbol "<"

means that the left side is strictly smaller than the right side.

If we want to be more precise in the notation, we also should have a lower limit.

0lb < p < 55lb

Where the lower limit is because the weight of the luggage can not be zero or smaller than zero.

This is the inequality we wanted.

Now, how we represent this on a number line?

when we have:

x > a

We represent this with a open circle at x = a (this means that x = a is not a solution) and we draw an arrow to the right of a.

and for:

x < a

we represent this with an open circle at a, and we draw an arrow to the left of a.

And if we have:

a < x < b

we draw an open circle at x = a and another at x = b, and all the points between these circles will be solutions.

You can see the graph of the inequality below.

Part A)

(where the point of the arrow should not be there, and both circles should be white)

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

idk bring the function back   im not smart

step-by-step explanation: