Divide by 3.x6- 6
3 x
3
6
- 18
3
3 x6- 18
SECTION 2.8 Solving Linear Inequalities 155
3 is positive. Do NOT
reverse the direction
of the symbol.The solution set is 1 - q, - 62 .The graph is shown in FIGURE 22.
–10 –9 –8 –7 –6 –5 –4 –3
FIGURE 22(b)
Here, each side of the inequality must be divided by 4, a negative number,
which doesrequire changing the direction of the inequality symbol.
Divide by 4.
Reverse the symbol.x...- 2
- 4 x
- 4
...
8
- 4
- 4 xÚ 8
-
- 4 xÚ 8
4 is negative.
ChangeÚto ....The solution set 1 - q, - 24 is graphed in FIGURE 23.
–6 –5 –4 –3 –2 –1 0 1 2
FIGURE 23 NOW TRYOBJECTIVE 4 Solve linear inequalities by using both properties of
inequality.
NOW TRY
EXERCISE 3
Solve the inequality, and
graph the solution set.
- 5 kÚ 15
NOW TRY ANSWER
- 1 - q, - 34
–6–5–4–3–2–1 0Using the Multiplication Property of InequalitySolve each inequality, and graph the solution set.
(a)
We divide each side by 3, a positive number, so the direction of the inequality
symbol does notchange. (It does not matter that the number on the right side of the
inequality is negative.)
3 x6- 18
EXAMPLE 3
Solving a Linear Inequality
Step 1 Simplify each side separately.Use the distributive property to
clear parentheses and combine like terms on each side as needed.
Step 2 Isolate the variable terms on one side.Use the addition property
of inequality to get all terms with variables on one side of the in-
equality and all numbers on the other side.
Step 3 Isolate the variable.Use the multiplication property of inequality
to change the inequality to the form “variable ” or “variable ”
where kis a number.
Remember: Reverse the direction of the inequality symbol only when
multiplying or dividing each side of an inequality by a negative number.