Solve for a Variable in a Formula


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In these lessons, we will learn how to solve a formula for a variable. It is also called solving literal equations.

Solving for a variable in a formula involves similar steps to solving for a variable in an equation. Let us review the steps as follows when we need to solve for a variable in a formula.

  1. Determine which variable you need to solve or isolate.
    To solve or isolate a variable means to get the variable on one side of the equation by itself.
  2. Use inverse operations to move all the other variables or constants to the other side of the equation. In order to keep the equation balanced, the operations need to be applied to both sides of the equation.

solve for variable
 

Example:

The formula for the area of a circle is A = πr2. Solve for r in the formula.


 



Solving a Formula For a Variable This algebra video lesson explains how to solve a formula for a variable.
The formulas include the area of a trapezoid formula, ohm’s law with voltage current and resistance.
The equivalent resistance of two resistors in a parallel circuit.
The geometric mean formula of two numbers.
The time it takes for two people to complete a job working together formula.
The area of a circle formula. The volume of a sphere formula.
The electromotive force of a battery along with internal resistance.

How to solve a formula with variables for a specified variable?
Examples:

  1. Solve for r
    d = rt
  2. Solve for h
    A = 1/2 bh
  3. Solve for b2
    A = 1/2(b1 + b2)
  4. Solve for w
    P = 2L + 2W
  5. Write y in terms of x
    y - 3 = 1/3(x - 4)
  6. Solve for a
    1/a + 1/b = 1/2


Solving formulas for given variables
Examples:

  1. c = ipv, solve for v
  2. p = a + 3b + 2c, solve for a
    t = 3j + 3v, solve for k

Solving an Equation for a Specified Variable
Examples:

  1. Solve for Solve for b1
    A = 1/2h(b1 + b2)
  2. Solve for z
    3z + x - y = 2x + 4

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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