Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

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. 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.
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