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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we will start learning about linear equations. Can anyone tell me what a linear equation is?
Is it an equation that makes a straight line when graphed?
Exactly! Linear equations have variables and constants that, when graphed, form a straight line. Can you name the components of a linear equation?
Variable and constant?
And coefficients!
Correct! Now let’s look at the process we'll use to solve them.
The first step in solving a linear equation is balancing operations. This means whatever you do to one side of the equation, you must do to the other side. Can anyone give an example of this?
If I add 5 to one side, I have to add 5 to the other side too!
Exactly! It keeps the equation equal. Remember the acronym B.O. for Balance Operations. Let's practice!
Now let's move on to the second step: isolating the variable. This is where we want the variable to be on one side of the equation alone. How do we do that?
We move other terms to the opposite side using balancing!
Correct! For instance, if we solve 3x + 5 = 20, we would subtract 5 from both sides to get 3x = 15. What comes next?
Then divide by 3 to isolate x!
Great job! Isolating the variable is key. Remember the saying: 'Isolate to calculate!'
Finally, we reach our last step: finding the solution. In our example, after isolating, we found that x equals what?
Five!
Right! And it's important to check our solution. Can someone show me how to check it?
We can plug it back into the original equation to see if it holds true!
Exactly! Always check your work. That’s the solving steps in a nutshell.
To balance, to balance, both sides must be fine, do the same to each side and the answer will shine.
Imagine a balancing scale where one side has apples and the other side must have the same. If you add 3 oranges to one side, you must add 3 to the other to keep it balanced.
Use B.O.S. to remind us: Balance, Isolate, Solve.
B.I.S. = Balance, Isolate, Solve.
Term
What is a linear equation?
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Term
What does it mean to balance an equation?
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An equation that forms a straight line when graphed, typically written in the form y = mx + b.
The process of performing the same operation on both sides of an equation to maintain equality.
To rearrange an equation to have the variable alone on one side.
The value of the variable that satisfies the equation.
This section outlines the systematic steps to solve linear equations, emphasizing balancing operations and isolating variables.
In this section, students will learn the steps involved in solving linear equations systematically. Key concepts include balancing operations on both sides of the equation, isolating the variable, and finding the solution. An example illustrates these steps in action, providing practical understanding.
In this section, we focus on the key steps involved in solving linear equations, which are fundamental for mastering algebra. The process can be broken down into three primary steps:
To illustrate these concepts, we walk through a word problem example: "If 3 times a number plus 5 equals 20, find the number." The equation 3x + 5 = 20 will be solved using the outlined steps, resulting in the solution where x = 5. Understanding these solving steps is essential for tackling more complex algebraic equations in future topics.