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Grade 9:  The Learning Equation Math

22.02 Linear Equations 1

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Variables and Equations

Refresher pp 34-35


SeekAWord2ech.class Author

Prerequisite Skills:

Key Terms         

algebraic equation, solution, root, simplify, substitution, evaluate, verify, variable, term, constant, isolating the variable, numerical coefficient

Learning Outcomes:      Review     Enrichment      Key Terms     Prerequisite Skills

The student will:

Algebra Tile Review

Algebra tiles have a variety of other names: algetiles, math tiles, and virtual tiles.  Algebra tiles can help you visualize equivalent algebraic expressions and/or equations.  Many of the real tiles have a positive and a negative side. The virtual algebra tiles activities will use multi-coloured positive tiles. The reverse (negative) side of each of these tiles is red. It helps to understand that negative tiles have one positive and one negative dimension.

Some algebra kits use black tiles for positive areas and red for the flip (negative) sides. Click the "Black/Red Tiles" button for additional information.



Algebra Tiles and the Distributive Property




What are Linear Equations?


Review of 1-step and 2-step Linear Equations

Linear Equations 1

ax + b = cx + d

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

The "Algebra Tiles Practice" includeds question generators for various linear equations. Select "ax + b = cx + d" to generate Linear Equations 1 examples. You may use the virtual tiles provided to generate a solution. The step buttons provided on the right show sample solutions 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:

ax + b = cx + d

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

A sample has been entered for you.  Get additional examples by clicking .

Solve   for 



Review        Learning Outcomes       Enrichment        Key Terms        Prerequisite Skills

Solve the equations in the this section independently.  If you have problems, look at the previous section again.

ax + b = cx + d

This activity will create the question.  You will need to complete the intermediate step(s) mentally or on paper, and provide the answer to the equation.

Instructions for using this page:

  • Click to get a randomly created problem with the form:

ax +b = cx + d

  • Enter your solution in the box.
  • Click .
Enter your solution :     x =

    x  = 

Score so far :    out of     .        Percentage =



Enrichment        Learning Outcomes       Review        Key Terms        Prerequisite Skills


What are Linear Equations?




The Cartesian plane was introduced to mathematics by René Decartes (1596-1650).


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