How to solve for x when there are 2 x terms on both sides of the equation.


In this hub you will be shown how to solve equations with unknowns (basically x’s) on both sides of the equation. Make sure you can solve simple equations requiring 1 or 2 inverses before you attempt this lesson.

The easiest way to do solve equations with unknowns on both sides of the equation is to remove the x term on the right hand side of the equation. So say if you have 4x on the right hand side then you need to subtract 4x from both sides or if you had -3x on the right hand side of the equation then you need to +3x on both sides. This will cancel out the x term on the right hand side of the equation.

Once the x’s are removed on the right hand side then you are left with a simple equation that you should be able to solve. Also, remember to work down your page!

Example 1

Solve 8x + 4 = 3x + 49.

Remove the 3x from the right hand side by taking 3x from both sides:

8x + 4 = 3x + 49 (take 3x from both sides)

5x + 4 = 49

Note that the 3x disappears on the right hand side (since 3x -3x = 0) and on the left hand side 8x is changed to 5x (since 8x – 3x = 5x).

Now just apply your number inverses to find the value of x:

5x + 4 = 49 (take 4 from both sides)

5x = 45 (divide both sides by 5)

x = 9

Example 2

Solve 6x + 2 = 73 – 4x

Remove the -4x from the right hand side by adding 4x to both sides:

6x + 2 = 73 – 4x (add 4x to both sides)

10x + 2 = 73

Note that the -4x disappears on the right hand side (since -4x +4x = 0) and on the left hand side 6x is changed to 10x (since 6x + 4x = 10x).

Now just apply your number inverses to find the value of x:

10x + 2 = 73 (take 2 from both sides)

10x = 71 (divide both sides by 10)

x = 7.1

Example 3

Solve 3x + 20 = x – 14

Remove the x from the right hand side by taking x from both sides:

3x + 20 = x – 14 (take x from both sides)

2x + 20 = -14

Note that the x disappears on the right hand side (since x -x = 0) and on the left hand side 3x is changed to 2x (since 3x – x = 2x).

Now just apply your number inverses to find the value of x:

2x + 20 = -14 (take 20 from both sides)

2x = -34 (divide both sides by 2)

x = -17

Now have a go at these 2 questions:

Solve these two equations:

a) 5x + 1 = -4x + 73

b) 3x -1 = 5x – 15

Answers

a) 5x + 1 = -4x + 73 (add 4x)

9x + 1 = 73 (take 1)

9x = 72 (divide by 9)

x = 8

a) 3x -1 = 5x – 15 (take 5x)

-2x – 1 = -15 (add 1)

-2x = -14 (divide by -2)

x = 7

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