Question

I just need to know the answer for question 12

Answer 1

Given:

The given inequalities are:

`3x+1>7\text{ and 4x}\leq24`

Solving first inequality, we get:

`\begin{gathered} 3x+1>7 \\ 3x>7-1 \\ 3x>6 \\ x>(6)/(3) \\ x>2 \end{gathered}`

Solving the second inequality, we get:

`\begin{gathered} 4x\leq24 \\ x\leq(24)/(4) \\ x\leq6 \end{gathered}`

Merging the solutions of both inequalities, we get:

`\begin{gathered} x>2\text{ and x}\leq6 \\ \Rightarrow x\epsilon\text{ (2,6\rbrack} \end{gathered}`

So, the graph will be a number line with an open circle at 2 and a closed circle on 6 and shading in between.

Therefore,

Option A is correct.