-27x - 60 > 15x - 20
+27x +20 +27x +20
-40= 42x
-20
----- = x Is this correct?
21
To factor x²-2x-4, you are looking to answer three questions.
1) What pair of numbers multiplies to 4?
2) What pair of numbers multiplies to 1?
3) Do these pairs when multiplied together, add/subtract to the middle term?
To answer (1), our pairs are 2 and 2, 4 and 1. Since there's a negative with 4 at the end (from question one), the signs will be opposite.
To answer (2), only pair multiplies to 1 - 1 and 1. Let's try both pairs from 1.
(x-4)(x+1) The middle term here is -3x. Nope.
(x-1)(x+4). The middle term here is 3x. Nope.
(x-2)(x+2) The middle term is 0x (or no middle term). Nope.
So x²-2x-4 does not factor.
Problem 1
With limits, you are looking to see what happens when x gets closer to some value. For example, as x gets closer to x = 2 (from the left and right side), then y is getting closer and closer to y = 1/2. Therefore the limiting value is 1/2
Another example: as x gets closer to x = 4 from the right hand side, the y value gets closer to y = 4. This y value is different if you approach x = 0 from the left side (y would approach y = 1/2)
Use examples like this and you'll get the results you see in "figure 1"
For any function values, you'll look for actual points on the graph. A point does not exist if there is an open circle. There is an open circle at x = 2 for instance, so that's why f(2) = UND. On the other hand, f(0) is defined and it is equal to 4 as the point (0,4) is on the function curve.
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Problem 2
This is basically an extension of problem 1. The same idea applies. See "figure 2" (in the attached images) for the answers.
The answer is -40 because if you get rid of the negative sign and add instead of subtract... you get 40 so its like adding in the opposite direction.