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Linear equations in one variable. Solved examples

Linear equations in one variable. Solution

Example.

Solve the equation

4x - 18 = 26 + 2x

Solution.

To solve the equation, we have to find the value of the variable x.

As we see the terms containing the variable x are on either side of the equals sign.

And we need to gather all the terms containing the variable x on one side. Let it be the left-hand side of the equation.

To do that, we

1. Add 18 to the left- and right-hand side of the equation

4x - 18 + 18 = 26 + 2x + 18
4x = 44 + 2x

By this way, we eliminate -18 from the left-hand side.

2. Subtract 2x from the left- and right-hand side of the equation

4x - 2x = 44 + 2x - 2x
4x - 2x = 44
2x = 44

By this way, we eliminate 2x from the right-hand side.

So, we have gathered all the terms containing the variable x on the left-hand side of the equation

2x = 44

Now we want to get the x by itself. We isolate the variable x by dividing both sides of the equation by 2

2x ÷ 2 = 44 ÷ 2
x = 22

The solution of the linear equation is

x = 22

We should check the solution by substitution 22 into the original linear equation

4x - 18 = 26 + 2x
4 * 22 - 18 = 26 + 2 * 22
70 = 70

The left side equals the right side.

This means that the solution x = 22 is correct.