Texas Instruments TI-83 Plus Manual Book page 120

Chapter 4: Linear Inequalities
Linear Inequalities: Using Algebra
Objectives
To review one-step and two-step linear inequalities.
To review the Properties of Inequalities.
Math Highlights
This section opens with examples of solving linear inequalities of the forms, x + a < b, ax < b,
and ax + b < c for any relation <, , >, and . Word problems about an amusement park are
included for students to solve. The students also see the need to interpret the answers obtained
using the appropriate number set. For example, they find that they have to knock down at least
9 3/8 bottles to earn enough points for the best prize. They see that they need to interpret this
answer as at least 10 bottles in order to win the prize.
The inequality properties of addition, subtraction, multiplication and division are given. When
multiplying or dividing by a negative number, students are reminded about the reversal of the
inequality sign. They also are reminded of how to translate phrases such as "at least" and "at
most" to the appropriate relation in the
Common Student Errors
Students may have a hard time deciding which steps to follow to solve the inequality. They
should connect this work back to the methods of solving linear equations. Students might
make sign errors as they add or subtract from both sides of the inequality or reverse the
inequality when multiplying or dividing by a negative number.
Students may have difficulty making the connection that C > 0 means C is positive and C < 0
means C is negative.
Although this section deals with the mechanical way of finding the solution set, students
should be reminded that they should check to see if the solution set is reasonable. They need
to keep using number sense.
Many students are able to find the answer using number sense without the written work.
Learning how to write mathematics correctly is part of the communication skill and needs to
be encouraged. This can cause frustration for students who find the problems easy to solve
"in their heads."
Some students have difficulty remembering the meaning of the symbols, <, , >, and . They
also have trouble translating the phrases such as "at least" and "at most."
Topics in Algebra 1
subsection.
Observations
© 2001 Texas Instruments
Section 2: Using Algebra
Teacher Notes
Teacher Notes 4-17