Question

Hello! I need some help with this homework question posted below. Q17

Answer 1

To solve an inequality, we need to isolate the value of x, and to do so we will perform a series of calculations in such a way that it remains the inequality unchanged, or at least still true.

To do so, we will perform first a sum of 2x to both sides of it, as follows:

`\begin{gathered} 7-2x+2x\ge3+2x \\ 7\ge3+2x \end{gathered}`

Now, we subtract 3 from both sides:

`\begin{gathered} 7-3\ge3+2x-3 \\ 4\ge2x \end{gathered}`

To finish it, we divide both sides by 2:

`\begin{gathered} (4)/(2)\ge(2x)/(2) \\ \\ 2\ge x \end{gathered}`

In another way, we can express the following:

`\mleft\lbrace x|x\le2\mright\rbrace or(-\infty,2\rbrack`

It means that the solution is option B.

To solve the second part, we need a filled line that comes from the negative infinity and goes until 2, but it must be including the number 2, and for this reason, the correct answer in the second part is:

D.