Question

Which of the followingrepresents this inequality?|2x + 6| > 3xA,b,c,d or e

Answer 1

To answer this question, we will consider the following cases:

1.-

`x\leq0.`

If

`\begin{gathered} x\\e-3, \\ |2x+6|>0>3x. \end{gathered}`

If

`\begin{gathered} x=-3, \\ |2*-3+6|=0>3*-3. \end{gathered}`

Case 2.

`x>0.`

Recall that:

`|a|>b,\text{ if and only if }a>b\text{ or -a}>b.`

Therefore:

`2x+6>3x\text{ or -}2x-6>3x.`

Solving each inequality for x, we get:

`\begin{gathered} 2x+6>3x, \\ 6>x, \\ -2x-6>3x, \\ -5x>6, \\ x>-(6)/(5). \end{gathered}`

The union of the solutions in the number line is represented as follows:

Answer: None of the above.