Question

How do I plot this And is my answer correct

Answer 1

We are given the following inequality:

$-38\le-6-2x$

To solve for "x" we will add 2x to both sides:

$-38+2x\le-6$

Now we will add 38 to both sides:

$\begin{gathered} 2x\le-6+38 \\ 2x\le32 \end{gathered}$

Now we divide both sides by 2:

$\begin{gathered} x\le\frac{32}{2} \\ \\ x\le16 \end{gathered}$

Therefore, the solution is the values of "x" that are smaller or equal to 16. This can be represented in the real line as follows:

We need to use all the points that are smaller (to the left) than 16. To represent the fact that 16 is also included in the solution we use a point on top of it.

In the case that 16 was not included then we would use a hollowed point on top of it.