Question

How do I solve inequalities and graph their solutions afterwards

Answer 1

$\begin{gathered} \text{Given} \\ 6x<-11 \end{gathered}$

Solve for x, by dividing both sides by 6

$\begin{gathered} 6x<-11 \\ \frac{6x}{6}<\frac{-11}{6} \\ x<-\frac{11}{6} \end{gathered}$

Now that we know that the solution is x < -11/6, to graph it, create a number line, and then locate -11/6, which is approximately -1.833, which is between -2, and -1, but closer to -2.

Since the inequality is less than ( < ), draw a hole at the starting point -1.833, and then draw an arrow towards the left. Notice that the direction of the inequality sign less than ( < ), is the same direction of the arrow ( <=== ) that we also drew on the number line.