The inequality to solve is:
[tex]-3x+1<7[/tex]
Let's take "3x" to the right-hand side and "7" to the left-hand side:
[tex]\begin{gathered} -3x+1<7 \\ 1-7<3x \\ -6<3x \end{gathered}[/tex]
Now, dividing by "3" we can solve for x. Then just re-arrange the inequality with variable on the left-hand side (as in convention). Shown below:
[tex]\begin{gathered} -6<3x \\ -\frac{6}{3}<\frac{3x}{3} \\ -2-2 \end{gathered}[/tex]
x is greater than negative 2
So, the number line will have an "open circle" at x = -2 and all numbers GREATER (right hand side) will be shaded.
The number line is shown below:
