MathematicsClass 7Simple Equations
Solving Equations by Balancing
Finding the root of an equation by performing identical operations on both sides.
Class 7 · MathematicsCBSE & ICSE SOF IMO
Definition
Solving an equation by balancing means performing the same mathematical operation on both sides of the equation to maintain equality. The goal is to isolate the variable on one side step by step. Whatever is done to the Left Hand Side (LHS) must also be done to the Right Hand Side (RHS).
Worked examples
1
To solve x - 3 = 5, add 3 to both sides to get x - 3 + 3 = 5 + 3, which results in x = 8.
2
To solve 4x = 20, divide both sides by 4 to get (4x)/4 = 20/4, which gives x = 5.
3
To solve x/2 = 6, multiply both sides by 2 to get (x/2) * 2 = 6 * 2, yielding x = 12.
Common mistakes
- • Applying an operation to only one side of the equation instead of both sides.
- • Using the wrong inverse operation, such as dividing when you should subtract or add.