Solve the inequality and graph the solution. (See Examples 1–3.)
−2b > 0
Example 1
Solve 3x + 5 > 11. Graph the solution.
Solution
First add −5 to both sides:
Now multiply both sides by 1 /3:
(Why was the direction of the inequality symbol not changed?) In interval notation (introduced in Section 1.1), the solution is the interval (2, ∞), which is graphed on the number line in Figure 1. The parenthesis at 2 shows that 2 is not included in the solution.
As a partial check, note that 0, which is not part of the solution, makes the inequality false, while 3, which is part of the solution, makes it true:
FIGURE 1
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