Solving Linear Equations with 1 variable – Review – Tutorial and Practice Questions

Linear equations with variable x is an equation with the following form:

ax = b

where a and b are some real numbers. If a = 0 and b is different from 0, then the equation has no solution.

Let’s solve one simple example of a linear equation with one variable:

4x – 2 = 2x + 6

When we are given this type of equations, we are always moving variables to the one side, and real numbers to the other side of the equals sign. Always remember: if you are changing sides, you are changing signs. Let’s move all variables to the left, and real number to the right side:

4x – 2 = 2x + 6

4x – 2x = 6 + 2

2x = 8

x = 8/2

x = 4

When 2x goes to the left it becomes now -2x, and -2 goes to the right and becomes +2. After calculations, we find that x is 4, which is a solution of our linear equation.

Let’s solve a little more complex linear equation:

(2x – 6)/4 + 4 = x

2x – 6 + 16 = 4x

2x – 4x = -16 + 6

-2x = -10

x = -10/-2

x = 5

We multiply whole equation by 4, to lose the fractional line. Now we have a simple linear equation. If we change sides, we change the signs. At the end we do the final calculations.