Lesson 9 — Activity 1: One-Step Equations
Lesson 9 — Activity 1: One-Step Equations
Getting Ready
The ability to rearrange formulas or rewrite them in different ways is an important skill in mathematics. The lessons that follow will explain how to rearrange some simple formulas.
In algebra, there are different ways to solve an equation depending on the type of equation. The first way is called the one-step method. This is where you have a very simple equation to solve.
For example, look at the equation x + 4 = 6.
Your goal is always to get the variable (also called the subject), the x, by itself. In order to do this, you would subtract 4 from both sides to get the answer as follows:
x + 4 – 4 = 6 – 4
x + 0 = 2
x = 2
This is called a one-step method, or one-step equation, because you only have to subtract 4 from both sides to get an answer.
When rearranging formulas, you must follow these rules:
RULE #1: You can add, subtract, multiply, and divide by anything as long as you do the same thing to both sides of the equals sign.
Whatever you do to one side of the equation, YOU MUST do to the other side of the equation.
You need to keep the equation in balance. For example, if you add 5 of something to one side of the balance, you have to add the same amount to the other side to keep the balance steady. The same thing goes for an equation — doing the same operation to
both sides keeps the meaning of the equation from changing.
RULE #2: To move or cancel a quantity or variable on one side of the equation, perform the "opposite" operation with it on both sides of the equation.
For example, if you had g – 1 = w and wanted to isolate g, add 1 to both sides:
g – 1 + 1 = w + 1
Simplify (because -1 + 1 = 0), therefore you end up with
g = w + 1
Another example would be g – 18 = 8
In this case, you would add 18 to both sides to get the answer as follows:
Whatever you do to one side of the equation, YOU MUST do to the other side of the equation.
You need to keep the equation in balance. For example, if you add 5 of something to one side of the balance, you have to add the same amount to the other side to keep the balance steady. The same thing goes for an equation — doing the same operation to both sides keeps the meaning of the equation from changing.
For example, if you had g – 1 = w and wanted to isolate g, add 1 to both sides:
g – 1 + 1 = w + 1
Simplify (because -1 + 1 = 0), therefore you end up with
g = w + 1
g – 18 + 18 = 8 + 18
g = 26
g = 26
Click here to play a game where you will add and subtract one-step equations!
You can also do one-step equations that deal with multiplication.
For example: 4h = 24
You would divide both sides by 4 to get the variable by itself and solve the equation as follows:
4h = 24
4 4
h = 6
4 4
h = 6
Or, if you were given a division question such as:
k = 2
4
You would multiple both sides by 4 to get the variable by itself.
(4)
k = 2(4)
The 4s on the left-hand side cancel out, leaving the variable by itself and you are left with:
k = 2(4)
k = 8
In order to remember what steps to take to get the variable by itself, it is helpful to practise working with these types of equations.
k = 2(4)
k = 8
k = 8
Self-check!
Try this!
Try this activity where you will practice working with one-step equations
Solve for x in the following equations:
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Subtract 12 from both sides
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Subtract 12 from both sides
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Add 9 to both sides
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Add 9 to both sides
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Multiply both sides by 2
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Multiply both sides by 2
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Divide both sides by 4
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Divide both sides by 4
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Digging Deeper
Click on the Play button below to watch a video on how to add and subtract using the one-step method.
Click on the Play button below to watch a video on how to multiply and divide using the one-step method.