1. ## inequality

Solve the compound inequality and write answer in INTERVAL notation:
5x > -9 + 2x and 9 – 2x >11

The equation y = 0.50x + 8 represents the cost, y, in dollars of a medium pizza at a local restaurant, where x represents the number of toppings.
(a) what is the y-intercept for this model and what does it represent in real-life?

(b) what is the slope of this model and what does this represent in terms of the cost of a pizza?

2. ## interval notation

Originally Posted by leleirvin
Solve the compound inequality and write answer in INTERVAL notation:
5x > -9 + 2x and 9 – 2x >11
5x > -9 + 2x
3x > -9
.x > -3

9 – 2x > 11
....
-2x > 2
.....-x > 1
......
x < -1 (thanks rgep!)

So we know that x must be greater than -3 and x must be less than -1. I beleive in interval notation that looks like this:

(-3,-1)

3. Oops!

-x > 1
x < -1

so the values of x satisfy -3 < x, x < -1 which is the interval (-3,-1)
(round brackets because the endpoints are not included).

4. Originally Posted by leleirvin
The equation y = 0.50x + 8 represents the cost, y, in dollars of a medium pizza at a local restaurant, where x represents the number of toppings.
(a) what is the y-intercept for this model and what does it represent in real-life?

(b) what is the slope of this model and what does this represent in terms of the cost of a pizza?
A)
y = 0.50x + 8

first find the y-intercept (or when x=0)

y = 0.50*(0) + 8

y = 8

Since x represents the number of toppings and y represents the cost of pizza, the y-intercept represents the cost of a pizza with no toppings. Since you can't have negative toppings this also represents the cheapest pizza you can have.

B)
y = 0.50x + 8 is in the form y = mx + b, where m is the slope.

In this case the slope = 0.5 which is the cost per additional topping for a pizza.