Inequalities
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Multi-Part
Lesson 4Get ConnectEDGLE 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.244 Equations and InequalitiesMain Idea
Solve inequalities by
using the Addition and
Subtraction Properties
of Inequality.Solve Inequalities by Addition
or Subtraction
MAIL A first class stamp can be used for
letters and packages weighing thirteen
ounces or less. Fisher is mailing pictures to
his grandmother, and only has a first class
stamp. His envelope weighs 2 ounces. How
much can the pictures weigh so that Fisher
can use the stamp?- Let x represent the weight of the pictures.
Write and solve an equation to find the
maximum weight of the package. - Replace the equal sign in your equation
with the less than or equal to symbol, ≤. - Refer to Exercise 2. Name three possible values of x.
An inequality is a mathematical sentence that compares quantities.
Solving an inequality means finding values for the variable that make
the inequality true. In the situation above, any number less than or
equal to 11 is a solution. The solution is written as the inequality
x ≤ 11.You can solve inequalities by using the Properties of Inequality.Addition and Subtraction
Properties of Inequality
Words When you add or subtract the same number from each
side of an inequality, the inequality remains true.Symbols For all numbers a, b, and c,- if a > b, then a + c > b + c and a - c > b - c.
- if a < b, then a + c < b + c and a - c < b - c.
Examples 2 < 4 6 > 3
+ 3 + 3 - 4 - 4
5 < 7 2 > - 1These properties are also true for a ≥ b and a ≤ b.242_253_C04L4_895130.indd 244 12/31/09 4:05 PM