Which of the following is the solution set of the equation shown below? 2x(x+3)-5(x+3)=0
2 answers:
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Answer:
a.
b. x ≠ -5 (Vertical asymptote) and x ≠ 5 (Hole)
Step-by-step explanation:
Factor the numerator (Grouping):
Two numbers that multiply to -30 and add to -7 = -3 and 10
Factor the denominator (Difference of Two Squares):
=
Factored Expression:
(x - 5) can be factored out of top and bottom as a hole-
Variable Restrictions:
Denominator ≠ 0
Vertical asymptote at x = -5 ⇒ x ≠ -5
You can see that each time x increases by 1, y increases by 5. This means that the coefficient of x is 5 (if you graphed it, the slope would be 5). To find what value to add at the end, you can look at what y is when x equals 0. In this case, that is -2 (on a graph, -2 would be the y-intercept).