Question

Which value would make the statement true 2/?>4/12​

Answer 1

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

Answer 2

Answer: Interval Notation (0, 6)

Graph: 0 o--------------o 6

Explanation:

`(2)/(x)>(4)/(12)\implies (2)/(x)>(1)/(3)\\\\\text{Restriction: Since the denominator cannot be zero, }x\\eq 0\\\\\text{First, set the left side EQUAL to the right side and solve:}\\(2)/(x)=(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}`

`\text{Now, plug each of the test points into the inequality to see which one(s)}\\\text{make a true statement.}\\\\(2)/(-1)>(1)/(3)\implies -2>(1)/(3)\quad FALSE\\\\\\(2)/(1)>(1)/(3)\implies 2>(1)/(3)\quad \boxed{TRUE!}\\\\\\(2)/(8)>(1)/(3)\implies -2>(1)/(3)\quad FALSE`

So, the solution is: every value between 0 and 6