Question

геWhich of the following facts did you include in yourexplanation? Check all of the boxes that apply.The value of c could be 5 or any numbergreater than 5.The solution is the intersection of bothsolution sets of the given inequalities.The solutions of the compound inequalitymust be solutions of both inequalities.

Answer 1

`C`

Step-by-step explanation:

Here, we start by solving each of the inequalities

Let us start with the left-hand side

We have that as follows:

`\begin{gathered} 2(2x-1)+7\text{ }<\text{ 13} \\ 4x-2+7<13 \\ 4x<13+2-7 \\ 4x<8 \\ x\text{ }<(8)/(4) \\ x<2 \end{gathered}`

For the right-hand side, we have the following:

`\begin{gathered} -2x+5\leq\text{ -10} \\ -2x\leq\text{ -10-5} \\ -2x\leq-15 \\ x\ge(15)/(2)\text{ or 7.5} \end{gathered}`

Now, let us plot a graph of the inequality as shown below:

The correct choice of option here is thus, the third option