Isolate a Variable

Isolating a variable is an algebraic technique. To isolate a variable is to rearrange and simplify and algebraic equation so that the variable you are trying to isolate is on one side of the equation and everything else is on the other side

For this article, we will be isolating the variable x in all example equations.

Steps

Single Variable Equations

1. Write down your equation.
2. Combine like terms. Group together all the terms with x and combine them, and group and combine the constants as well.
3. Simplify the equation.
4. Move terms with X's in them to the left side of the equation.
5. Move all parts of the equation except the terms that have an x in them to the the right side of the equation.
6. Divide both sides of the equation by the coefficient. The coefficient is the number that appears right before the variable. For example, in the term 6x, the coefficient would be 6, in the term 572x the coefficient would be 572, in the term -7x the coefficient would be =7, etc.
7. Solve for x.
8. Check your work. Plug your answer back into the equation for x and make sure that the equation yields a true statement.

Multi Variable Equations

1. Write down the equation.
2. Combine all like terms. For longer equations with more parts, try drawing different shapes around each type of term. For example, draw squares around all terms that have an x (5x, -2x, etc), triangles around terms with a y (6y, etc) and circles around constants. Make sure to include the sign on the coefficient! Then, group together all terms enclosed in the same shape. This can make combining like terms easier, as it is easy to see if you have left anything out.
3. Move all the terms that contain an x to the right side of the equation, and all other terms to the left side of the equation.
4. Divide both sides of the equation by the coefficient of x.
5. You have now isolated the variable x! However, there are still many other terms you will need additional information to solve for.

Things You'll Need

• Pencil/Pen
• Paper
• Math Homework/math problems

Sources and Citations

• How to Isolate a Variable - Original Source of text and images, shared with permission.

See also

• Use the Slope Intercept Form (in Algebra)
• Start Working with Continued Fractions
• Convert a Quadratic Formula to Roots Form by Completing the Square
• Factor Second Degree Polynomials (Quadratic Equations)
• Understand Linear Equations
• Understand Slope (in Algebra)
• Prove That the Square Root of Two Is Irrational
• Factor a Cubic Polynomial
• Calculate Frequency
• Find the Maximum or Minimum Value of a Quadratic Function Easily

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