# SBP-Program

## How to solve linear equations with fractions on one side

Example.

Solve the equation

 3x - 33 = 12 + 9x 2

Solution.

We are finding the value of the variable x to solve the linear equation.

First we collect all the terms containing x on the left side of the equation.

We subtract 9x from each side of the equation to eliminate the 9x from the right side

3x - 33 - 9x = 12 + 9x - 9x 2
3x - 33 - 9x = 12 2

We add 33 to each side of the equation to eliminate the 33 from the left side

3x - 33 - 9x + 33 = 12 + 33 2
3x - 9x = 45 2
3x 9x * 2 - = 45 2 2
3x 18x - = 45 2 2
-15x = 45 2

We need to obtain the x by itself. We isolate the variable x by dividing both sides of the equation by -15/2

-15x -15 -15 ÷ = 45 ÷ 2 2 2
x -15 -15 45 -15 * ÷ = ÷ 1 2 2 1 2
x 45 -2 * 1 = * 1 1 15
 -90 x = = -6 15

So, the solution of the linear equation is

x = -6

We should check the solution by substitution -6 into the original linear equation

 3x - 33 = 12 + 9x 2
 3 * (-6) - 33 = 12 + 9 * (-6) 2
 -18 - 33 = 12 - 54 2
-9 - 33 = −42
−42 = −42

So, the solution x = -6 is correct.