Algebra: Solve Linear Equation
In this course, students will learn the fundamentals of solving algebraic linear equations. We begin by understanding the definition of the balancing method and how it works. Students will then apply this technique to equations involving addition, subtraction, multiplication, and division. After mastering the basics, they will learn how to streamline their working by removing unnecessary steps and solving equations more efficiently.
Related Lessons:
What Is An Algebraic Equation?
Algebraic equation uses alphabetic letters to represent the unknown.
Lets say \(x+7=12\) where \(x\) is the unknown which we represent with an algebra.
Obviously, \(x=5\) since \(5+7=12\).
Now, \(6\times{y}=24\), where y is the unknown which we represent using an Algebra.
Therefore, y must be equal to 4 since \(6\times4=24\).
And we have just solve our first two algebraic equations.
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Balancing Eq - Addition & Subtraction
The “balancing equation” technique uses the definition of algebra to “move” algebra across the “=” sign. The basic approach is:
- What you do on the left, you do on the right
- What you do on the right, you do on the left.
The ideal of this approach is to reduce the number of terms in the algebraic equation till we get to the final answer.
In this video, we will see how to apply this technique for additional and subtraction of algebraic expression.
Similarly, for division and multiplication, we can do the same thing. We will run thru 2 questions on how to apply the “balancing equation” technique for division and multiplication.
Using the “balancing equation” technique exactly as it is can become inefficient. If we strictly follow the method by definition, we would need to repeatedly keep rewriting the same terms on both sides of the equation.
To make the process more efficient, we modified the method slightly.
The key approach remains the same: we remove terms from one side of the equation, whether the operation involves addition, subtraction, multiplication, or division. The rule is:
- What we say we will do on the left to remove an item, we do it on the right
- What we say we will do on the right to remove an item, we will do it on the left
This ensures the equation remains balanced while simplifying it step by step.
Now, what if we are given a fractional equation on both sides. For example, we are asked to solve the equation \(\frac{π}{3πβ2}=\frac{3}{7}\). The steps are:
- Cross multiply to remove the fractions
- Expand the algebraic expressions to remove the brackets
- Bring Algebra to the left, number to the right
- Solve for the unknown
Solving Multiple Fractional Algebraic Equation
What if we are asked to solve algebraic equations with multiple fractions? In this case, the first step is to remove all the denominators by multiplying all the terms with the LCM so that we have a linear equation. The steps are:
- Determine the LCM from all the denominators
- Multiple all the terms with the LCM. This will convert all the fractional terms to linear terms
- Expand the algebraic expressions to remove the brackets
- Add/Subtract the βlikeβ terms to simplify the expression
- Group algebra on the left, number on the right using the “Balancing Equation” technique
- Solve for the unknown