Before we get into the meat of our Solving Equations unit, we are going to quickly take a look at balancing equations.
As you begin solving equations in Algebra, the very first thing that you will learn is that whatever you do, you MUST keep your equation balanced!
It truly is the number one factor in solving equations!
You will see step-by-step how equations are kept balanced for every example in this unit! In the explanations, you will see the words:
Those are the key words for balancing equations! Let's take a look at a graphic to give you a better understanding.
Think of a scale that you would use to weigh things! If you put a 5 lb weight on the left side, what happens? Is the scale balanced? NO... of course not! What would you have to do to balance it perfectly? You'd have to put another five pound weight (or something that weighs five pounds) on the other side.
So... if I put 5 lbs one side, then I MUST also put 5 lbs on the OTHER side! That's the only way it will stay balanced!
So... does this phrase make sense...?
Think of the equation sign as the "center" of the scale.
Take a look at the picture above, and imagine two 5 lb weights on the left side, and two 5 lb weights on the right side. How much weight is on each side? 10 lbs, right? So, right now the scale is balanced!
Now, what happens if I take 5 lbs off of the right side? Is the scale balanced now? No, there's 10 lbs still on the left, but only 5 lbs on the right.
So, what must I do to keep it balanced? Yes.... I must ALSO take 5 lbs off of the left! Now, it is balanced again!.
So, in Algebra if you subtract 5 from one side, you must also subtract 5 from the other side.
Why have I continued to repeat those same words?
Because... those are the words that you MUST remember with EVERY step of EVERY equation that you solve!
You will see those words in all of my explanations, so look for them!
Keep those equations balanced and you will do well!
- Solving one-step equations (Addition).
- Solving one-step equations (Subtraction).
- Solving one-step equations (Multiplication).
- Solving one-step division equations.
- Solving two-step equations.
- Using the Distributive Property
- Solving equations with fractions
- Solving Literal Equations
- Equations with variables on both sides
- Writing equations given a word problem
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