Which inequality matches the graph? (2 points) A) −2x + 3y > 7

B) 2x − 3y < 7

C) −3x + 2y > 7

D) 3x − 2y < 7

  D)  3x − 2y < 7

Step-by-step explanation:

We note that the x- and y-intercepts are about 2.3 and -3.5, respectively.

In "intercept form," the equation of the line can be written ...

  x/x-intercept +y/y-intercept = 1

Using the given intercepts, this is ...

  x/2.3 +y/(-3.5) = 1

The answer choices suggest that we should multiply this by 7. When we do, we get ...

  3x -2y = 7 . . . . the equation of the boundary line

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The next trick is to figure the comparison symbol. We note that x-values are less than those on the line, and y-values are greater than those on the line. It is convenient to consider the term with a positive coefficient, so we don't get confused with minus signs and reversed comparisons.

As we said, x-values are less than those on the line, so the shaded area is ...

  3x -2y < 7 . . . . matches choice D

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3