Solving Decimal Equations

We will learn how to solve

• one-step equations involving decimals
• two-step equations involving decimals
• multi-step equations involving decimals
• equations with decimals and variables on both sides

Solving equations with decimals involves the same principles as solving equations with whole numbers or fractions.

If you prefer not to work with decimals you can first eliminate the decimals by multiplying by a multiple of 10. This can simplify the arithmetic and reduce the chance of decimal errors.

The following figure shows how to solve decimal equations with and without eliminating the decimals. Scroll down the page for more examples and solutions.

Algebra Worksheets
Practice your skills with the following Algebra worksheets:
Printable & Online Algebra Worksheets

1. Eliminate the Decimals
   Multiply every term in the equation by a power of 10 (10, 100, 1000, etc.) to convert all decimals into whole numbers. Choose the smallest power of 10 that eliminates all decimal places in the equation.
   Example:
   For the equation 0.3x + 0.7 = 1.5:
   The term with the most decimal places is 0.3, 0.7, and 1.5 (all have 1 decimal place).
   Multiply every term by 10:
   10 × 0.3x + 10 × 0.7 = 10 × 1.5
   

2. Solve the Simplified Equation
   Now, solve the equation as you would with whole numbers.
   Continuing the Example: 3x + 7 = 15
   Subtract 7 from both sides: 3x = 8
   Divide both sides by 3; x = 8/3
   

If you prefer to work with decimals then pay close attention to the decimal point during your calculations to avoid errors.
Example:
For the equation 0.3x + 0.7 = 1.5:
Subtract 0.7 from both sides: 0.3x = 0.8
Divide both sides by 0.3; x = 0.8/0.3 = 8/3

Solving One Step Equations Involving Decimals
This video provides four examples of solving one step linear equations involving decimals.

• Show Step-by-step Solutions

Solve a Two-Step Decimal Equation (Eliminate Decimals)
This video provides an example of solving a two-step equation with decimals by first eliminating the decimals.

• Show Step-by-step Solutions

Solve a Decimal Equation with Variables on Both Sides
This video provided an example of how to solve a multi-step linear equation in one variable with decimals and variables on both sides. This example shows how to first eliminate the decimals.

• Show Step-by-step Solutions

Solving Two Step Equations Involving Decimals
This video provides examples of solving two step linear equations involving decimals.

• Show Step-by-step Solutions

Solving Multiple Step Equations Involving Decimals
This video provides two examples of solving multiple step linear equations involving decimals.

• Show Step-by-step Solutions

Solving Multi-Step Equations with Decimals
This video covers solving multi-step equations that contain decimals. It includes three examples.

• Show Step-by-step Solutions

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