Rearranging Equations - Math Steps, Examples & Questions

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Updated: Dec 30, 2024

Lesson

Equations are the foundation of algebra, expressing relationships between different quantities. Rearranging equations, also known as solving for a variable, allows us to isolate any variable within an equation.

Its applications span across numerous fields, including physics, chemistry, engineering, and economics, where determining variables is crucial.

What Are Rearranging Equations?

Rearranging equations means moving things around to get the variable by itself. It is done to figure out what number "x" or the "variable" stands for.

We can add, subtract, multiply, or divide, but we need to do the same thing on both sides of the equation to keep it balanced. This helps us find the value of the unknown variable.

Example:

Isolate b in the equation a = bc.

Identify the operation: b is multiplied by c.
Apply the inverse: Divide both sides of the equation by c.

Simplify: This cancels out c on the right side, leaving b isolated.
So, a/c = b or b = a/c

How to Rearrange Equations

Rearranging equations involves isolating a specific variable by performing inverse operations. Here are the steps to rearrange equations-

1. Identify the variable you want to isolate.

2. Apply inverse operations:

Addition/Subtraction: To move a term added/subtracted to the variable, perform the opposite operation on both sides.

Example: In x + 3 = 7

subtract 3 from both sides: x + 3 - 3 = 7 - 3

resulting in x = 4.
Multiplication/Division: To move a coefficient (number multiplying the variable), divide both sides by that coefficient. If the variable is divided by a number, multiply both sides by that number.

Example: In 2y = 10

divide both sides by 2: 2y / 2 = 10 / 2

resulting in y = 5.
Powers/Roots: If the variable is raised to a power, take the corresponding root on both sides. If the variable is under a root, raise both sides to that power.

Example: In x² = 9