Solving an Equation Algebraically
Solving an Equation Algebraically introduces the systematic approach of identifying what operation has been applied to the variable and applying the inverse operation to both sides of the equation to isolate it, as taught in Yoshiwara Elementary Algebra Chapter 1: Variables. Grade 6 students learn that every algebraic manipulation must maintain equality by doing the same thing to both sides. This foundational skill underlies all equation-solving techniques in algebra.
Key Concepts
Property To solve an equation algebraically: 1. Ask yourself what operation has been performed on the variable. 2. Perform the opposite operation on both sides of the equation in order to isolate the variable.
Examples To solve $x + 9 = 20$, 9 is added to $x$. We do the opposite and subtract 9 from both sides: $x + 9 9 = 20 9$, so $x = 11$. To solve $8m = 40$, $m$ is multiplied by 8. We do the opposite and divide both sides by 8: $\frac{8m}{8} = \frac{40}{8}$, so $m = 5$. To solve $\frac{w}{4} = 6$, $w$ is divided by 4. We do the opposite and multiply both sides by 4: $4(\frac{w}{4}) = 4(6)$, so $w = 24$.
Explanation The main goal is to get the variable alone on one side of the equals sign. You do this by identifying the operation connected to the variable and using its inverse to cancel it out.
Common Questions
How do you solve an equation algebraically?
Identify the operation done to the variable, then perform the inverse operation on both sides to isolate the variable. For example, if x + 5 = 9, subtract 5 from both sides to get x = 4.
What does it mean to isolate the variable?
Isolating the variable means getting it alone on one side of the equation by undoing each operation that is attached to it.
Why must you do the same operation to both sides?
To keep the equation balanced. An equation is like a scale — any change on one side must be matched on the other to keep both sides equal.
Where is solving equations algebraically in Yoshiwara Elementary Algebra?
This foundational method is introduced in Chapter 1: Variables of Yoshiwara Elementary Algebra.
What inverse operations are used to solve equations?
Addition and subtraction are inverses, as are multiplication and division. Use these pairs to undo operations and isolate the variable.