Exercise 3 Page 58

To graph the solution set of an inequality on a number line, we need to follow three steps.

1. We place a circle on the number to which the variable is related.
2. If the inequality symbol is < or >, the circle is an open circle because the variable cannot equal that value. If the symbol is ≤ or ≥, the circle is a closed circle because the variable can equal that value.
3. Next, we shade the region on the number line either to the right or the left of the circle to show the solution set. If the symbol is < or ≤, we shade to the left of the circle, because the values to the left become smaller. If the symbol is > or ≥, we shade to the right of the circle, because the values to the right become larger.

x<7 We will place an open circle at 7 and shade the region to the left because x is less than 7.

Now consider a second inequality. x≥ 3 We will place a closed circle at 3 and shade the region to the right because x is greater than 3.