Answer:
When we have a quadratic equation:
a*x^2 + b*x + c = 0
There is something called the determinant, and this is:
D = b^2 - 4*a*c
If D < 0, then the we will have complex solutions.
In our case, we have
5*x^2 - 10*x + c = 0
Then the determinant is:
D = (-10)^2 - 4*5*c = 100 - 4*5*c
And we want this to be smaller than zero, then let's find the value of c such that the determinant is exactly zero:
D = 0 = 100 - 4*5*c
4*5*c = 100
20*c = 100
c = 100/20 = 5
As c is multiplicating the negative term in the equation, if c increases, then we will have that D < 0.
This means that c must be larger than 5 if we want to have complex solutions,
c > 5.
I can not represent this in your number line, but this would be represented with a white dot in the five, that extends infinitely to the right, something like the image below:
The absolute value would be 18 !
The least common denominator for the question you have supplied me with is 10. The least common multiple of the denominators, 5 and 10, is 10, making the LCD 10.
You are using the distributive property so you will multiply all the numbers in the parentheses by 5. So the end expression would be 30m+20n-15p
Two cheaper books = x
more expensive = 1.5x
so, 2.5x=150
150/2.5=x=60
therefore the more expensive book = 90