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Solving Multi-Step Equations

In these lessons, we will learn how to
  • Solve multi-step equations with whole numbers
  • Solve multi-step equations with fractions
  • Solve multi-step equations with decimals
Related Topics: More Algebra Lessons

Solving multi-step equations with whole numbers

To solve a multi-step equation, we would start by trying to simplify the equation by combining like terms and using the distributive property whenever possible.

Consider the equation 2(x + 1) – x = 5. First, we will use the distributive property to remove the parenthesis and then we can combine like terms and the isolate the variable.


Solve 2(x + 1) – x = 5


2(x + 1) – x = 5

2x + 2 – x = 5 (use distributive property)

x + 2 = 5 (combine like terms)

x + 2 – 2 = 5 – 2

x = 3

The following video shows more examples of solving multi-step equations.
Combine Like Terms. Distributive Property.

Multi-Step Equations.

Solving Multi-Step Equations With Fractions

To solve an equation with fractions, we first try to change it into an equation without fractions. Then, we can solve it using the methods we already know.

Consider the equation . To remove the fractions, we would need to multiply each term of the equation with the LCM of the denominator. In this case, we will multiply each term with 4. The 4 will cancel and we are left with equation 2x – 12 = 3. To isolate the variable, we will add 12 to both sides and then divide by 2.




The following video shows more examples of solving multi-step equations with fractions.
Solving Multi-Step Equations with Fractions & Decimals.

Solving Multi-Step Equations With Decimals

The steps involved in solving multi-step equations with decimals are the same as those in equations with whole numbers. The complication may lie more in the multiplication and division of decimals rather than the steps. Another method would be to multiply each term of the equation by ten (or hundred) to convert the decimals to whole numbers and then solve the equation.

The following video shows more examples of solving multi-step equations with decimals.
Solving Multiple Step Equations Involving Decimals
This video provides two examples of solving multiple step linear equations involving decimals.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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