7th Grade Math

Inequalities

PARTPART A BDEB C

Multi-Part

Lesson 4

Get ConnectED

GLE 0706.3.8

Use a variety of strategies

to efficiently solve linear

equations and inequalities.

SPI 0706.3.9 Solve linear

inequalities in one variable

with rational coefficients

symbolically or graphically.

Main Idea

Solve inequalities by

using the Multiplication

or Division Properties

of Inequality.

Solve Inequalities by

Multiplication or Division

SCIENCE An astronaut in a space suit

Location Astronaut (lb)Weight of

Earth 300

Moon 50

Pluto 67

Mars 113

Neptune 407

Jupiter 796

weighs about 300 pounds on Earth, but only

50 pounds on the Moon.

weight on Earth weight on Moon

300 > 50

If the astronaut and space suit each weighed

half as much, would the inequality still be

true?

1. Divide each side of the inequality 300 > 50 by 2. Is the inequality
   still true? Explain by using an inequality.


2. Would the weight of 5 astronauts be greater on Pluto or on Earth?
   Explain by using an inequality.

The examples above demonstrate how you can solve inequalities by

using the Multiplication and Division Properties of Inequality.

Multiplication and Division Properties

of Inequality, Positive Number

Words When you multiply or divide each side of an inequality by a

positive number, the inequality remains true.

Symbols For all numbers a, b, and c, where c > 0,

1. if a > b, then ac > bc and _ac > _bc.


2. if a < b, then ac < bc and _ac < _bc.

These properties are also true for a ≥ b and a ≤ b.

Multiply or Divide by a Positive Number

Solve 8x ≤ 40.

8 x ≤ 40 Write the inequality.

_^8 x

8

≤ _^40

8

Divide each side by 8.

x ≤ 5 Simplify.

The solution is x ≤ 5. You can check this solution by substituting

5 or a number less than 5 into the inequality.

weigh

Reading Math Reading Math The

inequality c > 0 means

that c is a positive number.

Lesson 4C Inequalities 249

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