Linear Equations Calculator

Enter the equation and the variable for which to solve. For example, enter 4x+5x=4 and x to solve the equation for x.


Solution:


Examples:

  • To solve 2x+3x=4, enter 2x+3x=4 and the variable x.
  • To solve \(\frac{2}{3}t+\frac{4}{3}t=3\), enter 2/3t+4/3t=3 and the variable t.

With this calculator, you can obtain the solution to a linear equation for a given variable. The solution will be displayed in the right panel.

How to use the linear equations calculator?

Step 1: Enter the linear equation in the first box. You can use any variable. If you enter an expression without the equals sign, the expression will be assumed to be equal to 0. For example, 2x+x+5, will be interpreted as 2x+x+5=0.

Step 2: Enter the variable to solve for in the second box. If the equation is 2x+x+5=0, you must enter x in the second box.

Step 3: Click “Solve” to get the solution for the entered equation.

Step 4: The solution will be displayed in the right panel.

What are linear equations?

Linear equations are equations where the variable has a maximum power of 1. For example, the equation 2x+4=3x is a linear equation. The equation x²+2x=4 is not a linear equation, since a term in the variable has a power greater than 1

Linear equations are characterized by having a unique solution. If you want to learn more about linear equations, you can look at our article.

How to solve linear equations?

To solve linear equations, it is necessary to apply operations so that the variable is completely cleared. For example, if we are adding 3 to the variable, we have to subtract 3 from both sides of the equals sign to isolate the variable.

Example 1: We want to solve the equation 3x+3=6. We can see that the left side (where the variable is) is being added by 3. So, we can subtract 3 from both sides of the equation to get 3x=3. We can then divide both sides of the expression by 3 to get x=1.

Example 2: We want to solve the equation 4x+2x=2+5. In this case, we have to start by simplifying the equation to get a simpler version. This means that we combine like terms to get 6x=7.

Now, we can divide both sides of the equation by 6 to completely isolate the variable and get x=7/6.

Example 3: Let’s solve the equation 2t+3t+2=5-t. Again, we start by simplifying the equation to get a simpler version. Then, combining like terms, we have 5t+2=5-t.

We see that we have variables on both sides. However, we can add t to both sides to get 6t+2=5. Now, we subtract 2 from both sides and we get 6t=3. Dividing both sides by 6, we get t=1/2.

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