Problem

Solve the inequality. Write the solution set in interval notation, and graph it. See Examp...

Solve the inequality. Write the solution set in interval notation, and graph it. See Examples.

EXAMPLE Solving a Linear Inequality
Solve 3x + 2 − 5 > − x + 7 + 2x, and graph the solution set.
Step 1 Combine like terms and simplify.
3x + 2 − 5 > − x + 7 + 2x
3x − 3 > x + 7
Step 2 Use the addition property of inequality.
Step 3 Use the multiplication property of inequality.
The solution set is (5, ∞). Its graph is shown in FIGURE 24.
FIGURE 24
EXAMPLE Solving a Linear Inequality
Solve 5(x − 3) − 7x ≥ 4(x − 3) + 9, and graph the solution set.
Step 1
Step 2
Step 3
The solution set is (−∞, − 2]. Its graph is shown in FIGURE 25.
FIGURE 25
EXAMPLE Solving a Linear Inequality with Fractions
Solve , and graph the solution set.
To clear fractions, multiply each side by the least common denominator, 6.
Step 1
Step 2
Step 3
Check that the solution set is (−6, ∞). See the graph in FIGURE 26.
FIGURE 26