Answer: Interval Notation (0, 6)
Graph: 0 o--------------o 6
Step-by-step explanation:
[tex]\dfrac{2}{x}>\dfrac{4}{12}\implies \dfrac{2}{x}>\dfrac{1}{3}\\\\\text{Restriction: Since the denominator cannot be zero, }x\neq 0\\\\\text{First, set the left side EQUAL to the right side and solve:}\\\dfrac{2}{x}=\dfrac{1}{3}\quad \text{cross multiply}\rightarrow 2(3)=x\quad \rightarrow \quad 6=x\\\\\\\text{Next, choose your test points}\\\bullet \text{to the left of 0: I choose -1}\\\bullet \text{between 0 and 6: I choose 1}\\\bullet \text{to the right of 6: I choose 8}[/tex]
[tex]\text{Now, plug each of the test points into the inequality to see which one(s)}\\\text{make a true statement.}\\\\\dfrac{2}{-1}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE\\\\\\\dfrac{2}{1}>\dfrac{1}{3}\implies 2>\dfrac{1}{3}\quad \boxed{TRUE!}\\\\\\\dfrac{2}{8}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE[/tex]
So, the solution is: every value between 0 and 6
2/x > 4/12
We can plug each of the numbers given in to verify.
2/4 = 4/8 = 6/12 > 4/12 √ this is correct
2/6 = 4/12 > 4/12 × this is incorrect
2/12 > 4/12 × this is incorrect
2/24 = 1/12 > 4/12 × this is incorrect
Your answer is A
