Solve the inequality and graph the solution. (See Examples 1–3.)−4a ≤ 36Example 1Solve 3x...

Solve the inequality and graph the solution. (See Examples 1–3.)

−4a ≤ 36

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