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Grade 9:  The Learning Equation Math

22.05 Linear Inequalities

Variables and Equations

Refresher pp 40-41

SeekAWord2ech.class Author

Prerequisite Skills:

 
 

Learning Outcomes:      Review     Enrichment      Key Terms     Prerequisite Skills

The student will:

Real and Integer Number Lines
To show {x : x< 3} on a real and integer  number line, we could use the graphs shown at right. Note that we use an open circle around 3 to show we don't want to include the 3.
Real
xlt3.gif (388 bytes)

The real numbers less than 3 are highlighted in purple. Notice the integers and all of the points between each pair of integers is included in the purple section. The arrow head is also in purple to indicate the pattern continues to the left.
Integer
xlt3.gif (388 bytes)

Only the integers less 3 are highlighted in purple. The arrow head is also in purple to indicate the pattern continues to the left.
The graph at right represents the set {x : x<-1}. Note that since we want to include -1, we shade in the circle around 1.
Real
xlem1.gif (380 bytes)

The real numbers less than or equal to -1 are highlighted in purple. Notice the integers and all of the points between each pair of integers is included in the purple section. The arrow head is also in purple to indicate the pattern continues to the left.
In the problems below , determine what set the graph shows by choosing the appropriate inequality and then filling in the correct number. Click Enter to get feedback to your answer.  The Help button has been programmed to show the steps for each problem. If the graph doesn't change when you go to a new problem, try scrolling up and down.

source:  NSU-Math 1030 Unit 1 Section 7   Author

 

 

What are Linear Equations?

 

Review of 1-step and 2-step Linear Equations

 

There are several example solutions using algebra tiles given in the "Introduction".

The "Algebra Tiles Practice" includeds question generators for various linear equations. Select one of the linear equation buttons to generate examples. You may use the virtual tiles provided to generate a solution. The step buttons provided on the right show sample soluitons as well.

Let's study how these tiles can be used to solve equations.

 

4 Methods for Solving Linear Questions

There are a variety of ways to solve linear equations.  Four methods for each type of linear equation is included below:

 

 

Soving inequalities follows the same rules as linear equalities except when you multiply or divide both sides by a negative number, the inequalilty sign reverses. 

ax + b > c

 

ax + b > c

  • Click on "show a problem".

  • Do the problem on paper.

  • Click on "show the answer".

  • Use "show step 2" to help correct your work.

  • Repeat until you can do the problems easily.

a/b
(1000th)

source:   Algebra 1-3

 

Soving inequalities follows the same rules as linear equalities except when you multiply or divide both sides by a negative number, the inequalilty sign reverses.

ax + b > cx + d

ax + b > cx + d

  • Click on "show a problem".

  • Do the problem on paper.

  • Click on "show the answer".

  • Use "show step 2" to help correct your work.

  • Repeat until you can do the problems easily.

Fraction:
Decimal (thousandth): 

source:   Algebra 1-4

 

Review        Learning Outcomes       Enrichment        Key Terms        Prerequisite Skills

 

Algebra

Practice Tests - Graphing Inequalities

Graphing Inequalities on a line graph:

Highlight the original line graph. Copy then paste it where you need the line graph. Change the colour of the graph & numbers in the appropriate manner. Add the arrow where it belongs. To make < or > click on underline in the text properties then use the < or > key on the keyboard. 
Original line graph
 
     ---|----|----|----|----|----|----|----|----|----|----|----|---
       -5   -4   -3   -2   -1   0    1    2     3    4    5    6
Line graph for x > -2, x is an integer
 
     ---|----|----|----|----|----|----|----|----|----|----|----|---->
       -5   -4   -3   -2   -1   0    1     2    3    4    5    6
 
Line graph for x > -2, x is a real number
 
     ---|----|----|----|----|----|----|----|----|----|----|----|--->
       -5   -4   -3   -2   -1   0    1     2    3    4    5    6
Line graph for x < -2, x is an integer
 
     <--|----|----|----|----|----|----|----|----|----|----|----|---
       -5   -4   -3   -2   -1   0    1    2    3     4    5    6
 
Line graph for x < -2, x is a real number
 
     <--|----|----|----|----|----|----|----|----|----|----|----|---
       -5   -4   -3    -2   -1   0    1    2    3     4    5    6

 

These exercises work only with Window 95 at this time.
Topic Exercise(s) from:

Interact Math:  Solving Inequalities
Determine if a number is part of the solution of an inequality.
1, 3
Graph an inequality on a number line
5, 7, 9, 11, 13
Solve, then graph an inequality.
15, 17, 19, 21, 23, 25, 27, 29, 31
 x<b
33, 35, 37, 39, 41, 43, 45, 47
ax<b, a+x>b,
ax+b>cx+d
49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83
ax+b<c, a(x+b)>c,
ax+b>cx+d, (a/b)x+c>d, and others

source of all of the exercises:  Introductory Algebra: InterAct Math: Chapter 2: Section 2.7

 

 

Enrichment        Learning Outcomes       Review        Key Terms        Prerequisite Skills

 

Enter an inequality along with the variable you wish to solve it for and click the button.

An example has been entered for you.  Additional examples can be generated by clicking

Solve   for 
Note:  |2x+5| means the absolute value of (2x+5).

Graph of Inequality - high level

 
 

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