Question

How do we show where an inequality is true on the number line! 50 points!

Answer 1

Usually, we use the number line to solve inequalities with the symbols, < , ≤ , >  , and ≥ .(the second and last one was rather hard to find on my keyboard) In order to solve an inequality using the number line, though, just turn the inequality sign to an equal sign. Then, solve the equation. Next step, graph the point on the number line (remember to graph as an open circle if the original inequality was <, or >). The number line should now be divided into 2 regions, one to the left of the graphed point, and one to the right of said point.

After that, pick a point in both regions and "test" it, check to see if it satisfies the inequality when plugged in for the variable. If it does, draw a darker line from the point into that region, with an arrow at the end. That is the solution to the equation: if one point in the region satisfies the inequality, the entire region will satisfy the inequality.

I had to check back in an old textbook to remember all of that. Sorry about the earlier answer. That was rather foolish to do so without actually understanding the question.