SBP-Program

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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
22
3x - 18x = 45
22
-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 = 45 ÷ -15
222
x * -15 ÷ -15 = 45 ÷ -15
12212
x * 1 = 45 * -2
1115
x = -90 = -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.