Is -3x-6 greater than x-2

Answer 1

That depends on the value of x. You can think of those two expressions as being linear functions:

f(x) = -3x - 6

g(x) = x - 2

To find the point at which they intersect (where f(x) = g(x)), we simply have to declare them as being equal and solve for x:

if f(x) = g(x) then:

-3x - 6 = x - 2

-4x = 4

x = -1

So the two functions intersect at the point where x = -1. If you plug that value into either function, you'll find that they return the value -3. This tells ups that these functions describe two lines that intersect at the point (-1, -3).

Given that the coefficient of our first function, "f" has a lower value than the function "g", we know that when the x value is greater than that of their point of intersection, "g" will return a greater value. Before our point of intersection, "f" will return a greater value.

So in answer to your original question, we can say:

if x < -1: yes

if x ≥ -1: no