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Solving Linear Equations; The four types anyone can learn

Solving Linear Equations

Tutorial for Solving Linear Equations

Solving Linear Equations, how anyone can learn

To understand solving linear equations we need to understand what our objective is and how to do it.  We will go over 4 types of linear equations but for each type our process will be the same.  Isolate the variable so it is equal to a quantity.  That quantity is our solution.

  1. Simplify the left and right side of the equation by applying distributive property or combining like terms. (If needed, one and two step equations you will skip this step)
  2. Use inverse operations to combine the variables on the same side. (It doesn’t matter which side, however my advice is to choose to have the variable on the side where it will have a positive coefficient)
  3. Identify the operations that are being applied to the variable and apply inverse operations to both sides to undo the operation being applied to the variable.(Follow the reverse order of operations, undo additional and subtraction before undoing multiplication and division)
  4. Check your answer by replacing your variable in the original equation with the value of the solution you solved for.

Those steps might have been to vague for you or to “mathy”.  No worries I have made a video that highlights each of those steps with multiple examples.

We must master using inverse operations and the properties of equality (basically doing the same operation to both sides) before we can start adding steps. So here we have it the first introductory video for solving linear equations.
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Solving one-step equations

So theres the basics. Most students understand solving one step equations but start getting confused with two step equations because of the reverse order of operations. So lets review

When we have two operations it is very important, I mean very important to follow the reverse order of operations. If you don’t believe me try solving any of the equations I have below not using the reverse order of operations and you will obtain a different answer. Solving the same equation and obtaining two different answers is not good. So we have rules people! To ensure all arrive at the same solution.

Again REMEMBER always undo addition/subtraction before you undo multiplication/division.

Solving Two-Step Equations

Feeling confident yet? You know that is a question you never want to answer because your teacher always wants to decide to give you harder or more problems for homework. We have more to learn though. Now we will go through equations where we have to simplify before we solve. By simplifying I mean if there are parenthesis, determine if they are needed, (a number is outside of them other than one) and if so, apply the distributive property. If there is more than one variable (on the same side) then combine them, just make sure you take note if they are positive or negative. Here are the examples I work through.

Solving Multi-Step Equations with the variable on the same side

Please remember when there are variables on opposite sides we cannot combine them like we did in the previous video. We still follow the first step in simplifying each side by applying the distributive property(if needed) and combining like terms but ONLY when they are on the SAME side. When we have variables on opposite sides we have to use inverse operations to eliminate a variable on one side.

I can try to explain it by writing but who am I kidding anyways. You just want to watch how its done not read math jargon. So here it is my final video of this post!

Solving Multi-Step Equations With The Variable On Opposite Sides

And there you have it! Remember you can always check your answer by plugging in the value of your solution back in for the variable of your original equation.  If it makes your equation true as you simplify both sides.  You have found your solution!

Please comment below if you have have further questions on this topic.

If you are in need of more resources I have provided the links to my courses that provide many more examples and resources for you to refine your skills.

Master Solving One Step Equations

Master Solving Two Step Equations

Master Solving a Multi-Step Equation(variable on same side)

Master Solving a Multi-Step Equation



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