SECTION 2.5 Linear Inequalities in One Variable 97
OBJECTIVE 4 Solve applied problems by using linear inequalities. The
table gives some common words and phrases that suggest inequality.
CAUTION In three-part inequalities, the order of the parts is important.For
example, do not write since this would imply that a false
statement. Write three-part inequalities so that the symbols point in the same direc-
tion and both point toward the lesser number.
86 x+ 26 3, 86 3,
Solving a Three-Part InequalitySolve and graph the solution set.
Add 1 to each part.Divide each part by.
Reverse the inequality symbols.- 2 ... x ...
1
3
1
3
Ú x Ú- 2
- (^1) - 3
- 3
Ú
- 3 x
- 3
Ú
6
- 3
- 1 ... - 3 x ... 6
- 2 + 1 ...- 3 x- 1 + 1 ... 5 + 1
- 2 ... - 3 x- 1 ... 5
- 2 ...- 3 x- 1 ... 5
EXAMPLE 7
Rewrite in the
order on the
number line.NOW TRY
EXERCISE 7
Solve and graph the solution
set.
- 2 6- 4 x- 5 ... 7
NOW TRY ANSWER
- C-3, -^34 B
–4 –3 –2 –1 0 13- 4
Check that the solution set is C-2,^13 D,as shown in FIGURE 16.
–3 –2 –1 0 13 1 2FIGURE 16 NOW TRYEquation or Inequality Typical Solution Set Graph of Solution Set
Linear equationLinear inequalityorThree-part inequality–1 2- 1 ... 5 x+ 4 ... 14 3 - 1, 2 4
25 x+ 4714 1 2, q 225 x+ 4614 1 - q, 2 225 x+ 4 = 14 526Word Expression Interpretation
aexceedsb
ais at leastb
ais no less than b
ais at most b
ais no more than ba...ba...baÚbaÚba 7 b