Linear Equation Solver for Solving Equations with 1 Variable

Linear Equation Solver Sign

This calculator will use the distributive and equality properties -- as well as combining like terms and inverse operations -- to solve linear math equations having one variable.

Specifically, this math equation solver will handle multiple distributions (maximum of 2 terms within each parenthesis) and simplifications involving the elimination of fractions and decimals (not radicals or exponents).

Plus, unlike other online math solvers, this calculator will show its work and give a detailed step-by-step explanation as to how it arrived at the result. This makes the solver especially useful for checking the answers you derive from solving the equations manually.

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Linear Equation Solver

Solve single variable linear equations containing integers, fractions, and/or decimals.

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Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Example linear equations:

Example linear equations:

To see an example of how the linear equation solver calculates a solution, select an equation from the drop down menu - which will enter the selection in the equation field for solving. To clear the equation field to enter your own equation, select "---ENTER MY OWN---".

Linear equation:

Linear equation:

Enter an equation that fits within the following guidelines:
  • No spaces between terms or operators.
  • One variable only and no radicals or exponents.
  • Parenthesis only for distribution and no more than 2 terms within a parenthesis, and no nested parenthesis (parenthesis inside parenthesis).
  • Numerators and denominators must be integers only (no expressions).
  • Decimal numbers can have a maximum of 2 decimal points.
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Calculated solution:

Calculated solution:

Below is the result calculated by the linear equation solver for the entered equation. Please substitute the calculated result for the variable to make sure the result is in fact a solution to the equation.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

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Help and Tools

Learn

What linear equations are and how to solve them.

What is a Linear Equation?

A linear equation is an expression that can be written in the form ax+b=0, where a and b are constants and x represents an unknown variable that, once found, will make the expression true.

The following are some basic examples of linear equations having one variable:

Linear Equation Examples

7x + 3 = 20

2(y + 1) - 4 = 4(y - 3)

16.5a + .25a = 25.1a

 1x+3=2x-4 
245

How to Solve Linear Equations

Solving linear equations is a process aimed at getting the variable by itself on one side of an equal sign and everything else on the other side. To explain how to solve linear equations, I will use an example equation that contains all 4 types of terms that can be handled by the linear equation solver.

Example equation:
3(x-1)+1/2=.25+4
First use the distributive property to get rid of the parenthesis:
3(x-1) = 3x-3
After removing parenthesis we are left with:
3x-3+1/2=.25+4
Remove the fractions by multiplying both sides of the equation by 2 (least common multiple of all denominators in equation):
2(3x-3+1/2)=2(.25+4)
After multiplying both sides by 2 we are left with:
6x-6+1=0.5+8
Remove decimals by multiplying both sides of the equation by 100:
100(6x-6+1)=100(0.5+8)
After multiplying both sides by 100 we are left with:
600x-600+100=50+800
Combine the like terms:
-600 + 100 = -500 and 50 + 800 = 850
After combining like terms we are left with:
600x-500=+850
Add 500 to both sides of the above equation to get constants on right side:
-500 + 500 = 0 and 850 + 500 = 1350
After adding 500 to both sides we are left with:
600x=1350
Get the variable by itself by dividing both sides by 600:
600x=1350
600600
After dividing both sides by 600 we are left with:
x=1350
600
Simplify the result:
x=1350=1350 ÷ 150=9or21
600600 ÷ 15044

Always Check to Make Sure Your Answer is a Solution

Regardless of which method or tool you use to solve linear equations, you should always check your results by substituting the result for the variable and seeing if the resulting equation proves to be true. After all, humans create math solvers, and humans make mistakes.

To make sure our answer to the above example linear equation is, in fact, a solution, let's substitute 9/4 for x and check to see if the resulting equation proves to be true:

Substitute Answer for Variable to Check Your Work

3(9/4 - 1) + 1/2 = .25 + 4

4(27/4 - 3/1 + 1/2) = 4(4.25)

27 - 12 + 2 = 17

15 + 2 = 17

17 = 17

The solution 9/4 is the solution to the example equation.

If you have any questions regarding the explanations on this page, please submit them using the feedback form located beneath the calculator.

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.