The inequality (14 is less than or equal to x) can also be written
(xis greater than or equal to 14). Notice that in each case the inequality symbol
points to the lesser number,14.
CHECK Related equation
Let
✓ True
So 14 satisfies the equality part of Choose 10 and 15 as test values.
Let Let
False ✓ True
10 is not in the solution set. 15 is in the solution set.
The check confirms that 3 14, q 2 is the correct solution set. See FIGURE 10.
34630 44645
14 + 211526 x=15.
?
14 + 211026 x=10. 31152
?
31102
14 + 2 x 63 x
....
42 = 42
14 + 21142 31142 x=14.
14 + 2 x= 3 x
14 ... x xÚ 14
SECTION 2.5 Linear Inequalities in One Variable 93
NOW TRY
EXERCISE 2
Solve and
graph the solution set.
4 x+ 1 Ú 5 x,
NOW TRY ANSWER
- 1 - q, 1 4
–2 –1 0 1 2
0 2 4 6 81610 12 14 18 20
FIGURE 10 NOW TRY
OBJECTIVE 2 Solve linear inequalities by using the multiplication prop-
erty.Solving an inequality such as requires dividing each side by 3, using
the multiplication property of inequality.
Consider the following true statement.
Multiply each side by, say, 8.
Multiply by 8.
True
This gives a true statement. Start again with and multiply each side by
Multiply by
False
The result, is false. To make it true, we must change the direction of the
inequality symbol.
True
As these examples suggest, multiplying each side of an inequality by a negative
number requires reversing the direction of the inequality symbol. The same is true for
dividing by a negative number, since division is defined in terms of multiplication.
167 - 40
16 6-40,
16 6- 40
- 21 - 82651 - 82 - 8.
- 26 5, -8.
- 16640
- 218265182
- 265
3 x... 15
Using the Addition Property of Inequality
Solve and graph the solution set.
Subtract 2x.
Combine like terms.
xÚ 14 Rewrite.
14 ... x
14 + 2 x- 2 x... 3 x- 2 x
14 + 2 x... 3 x
14 + 2 x... 3 x
EXAMPLE 2
Be careful.