Isolating Variable Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Isolating Variable.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Rearranging an equation by applying inverse operations until the variable stands alone on one side.

Peel away everything around x until only x remains: x = answer.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Apply inverse operations in reverse order to systematically undo everything done to the variable.

Common stuck point: Work in reverse order of operations: undo +/- first, then \times/\div.

Sense of Study hint: Write the operations done to x from inside out, then undo them in reverse order, one at a time.

Worked Examples

Example 1

easy
Isolate y in 2x + y = 10.

Solution

  1. 1
    Subtract 2x from both sides: y = 10 - 2x.
  2. 2
    Now y is alone on one side—it is isolated.
  3. 3
    This expresses y as a function of x.

Answer

y = 10 - 2x
Isolating a variable means getting it alone on one side of the equation. This is done by performing inverse operations on both sides.

Example 2

medium
Solve A = \frac{1}{2}bh for h.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Isolate x in x - 7 = 3.

Example 2

hard
Solve P = 2l + 2w for w.
← Back to Isolating Variable Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

inverse operationsequations