6th Grade Math Textbook, Fundamentals

Solve: a235.6 1200.7

a235.6 235.61200.7 235.6 Add 235.6 to both sides.

a1436.3

Check:Try a1436.3.

1436.3235.6 1200.7

1200.7 1200.7 False

So the solution set is all numbers greater than 1436.3.

Substitute 1436.3

for a.

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1

Try a1535.6.

1535.6235.6 1200.7

1300 1200.7 Tr u e

?

 Substitute

1535.6 for a.

Remember:

Addition Property of Inequality

For any real numbers a, b, and c,

if ab, then acbc.

Subtraction Property of Inequality

For any real numbers a, b, and c,

if ab, then acbc.

 &KDSWHU

14-9

Addition and Subtraction:

Inequalities with Rational Numbers

Objective To solve one-step inequalities using the Addition and Subtraction Properties

of Inequality• To graph the solution sets of inequalities involving rational numbers

A water ride at the amusement park limits each ride to a

maximum mass of 527.25 kg. The “boat” itself and its

equipment have a mass of 154.55 kg. What is the maximum

combined mass of passengers allowed for each ride?

To determine the maximum combined mass of passengers,

write and solve an inequality.

Let mthe passengers’ maximum mass.

m  154.55 527.25

Solve inequalities with rational numbers the same way that

you solve inequalities with integers. Remember to use the

properties of inequalities.

Solve: m154.55 527.25

m154.55 154.55 527.25 154.55

m 372.7

To check, choose two numbers from the solution set, and

substitute each into the inequality.

Check:Try m372.7.

372.7154.55 527.25

527.25 527.25 Tr u e

So the passengers’ maximum mass for each ride is at most 372.7 kg.

?

Substitute 372.7

for m.

Subtract 154.55

from both sides.

Boat’s

is at most maximum mass

Mass of boat

plus and equipment

Passengers’

maximum mass

Try m300.

300 154.55 527.25

454.55 527.25 Tr u e

Substitute 300

for m.

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