Solve the inequality and express in interval notation and graph its solution on a number line
1 answer:
Answer:
x ∈ (-∞, 3) U (6, ∞).
Step-by-step explanation:
We use factorization and optain
Then, we have two critical points: x=3 and x=6. Now:
(i) for x < 3 we have that x-6 <0 and x-3 <0. Then (x-6)(x-3) > 0.
(ii) for 3 < x < 6 we have that x -6 <0 and x -3 > 0. Then (x-6)(x-3) < 0.
(iii) for x > 6 we have that x-6 >0 and x-3 > 0. Then, (x-6)(x-3) > 0.
conditions (i) and (iii) satisfy the inequatliy, then the solution is x ∈ (-∞, 3) U (6, ∞).
The graph is in the picture below.
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The correct answer is A.
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A side note: Actually, option C has a constant of proportionality of two as well, except the roles of x and y are interchanged. I chose option A because usually you want the y = mx form, but the names of the variables are obviously meaningless.