Solve equations with unknowns on each side and with brackets
The method you use when solving equations will change depending on the equation you’re given, and its complexity, but the basic tools will always be simplifying both sides where possible, and rearranging terms (moving them to the other side of the equals side, and balancing the equation).
The following information will show you how to solve equations with an ‘unknown on both sides’, an equation with brackets, it will look something like this:
2x + 4 = 2(5x – 3)
To solve the equation given above, you will need to know how to expand brackets, how to rearrange equations, and how to collect like terms (simplify).
This example can be solved like this:
2x + 4 = 2(5x – 3)
2x + 4 = 10x – 6 (work out any calculation that will allow us to get rid of the brackets)
Rearrange to get all the numbers (on their own) on one side:
2x + 4 + 6 = 10x , (by doing this we must remember that if we move a positive number to the opposite side it will become negative and vice versa)
Rearrange to get all the like terms on to the other side:
4 + 6 = 10x – 2x (remember this will cause them to change to either positive or negative depending on what they were originally)
10 = 8x (work out the calculations on both sides)
10/8 = x (get x on it's own, we can do this by dividing the number infront of the x on both sides)
We usually prefer to write the letter first, so at this point we need to swap the sides around:
x = 10/8
Having a fraction as a solution is perfectly fine. If we want to convert it to a decimal, though, we can write:
x = 1.25
Let's try one more example, to make sure that you will be able to comfortably answer this type of question in your exam or in your worksheets!
Example: 4x + 10 = 4(8x - 6)
Step 1: Expand
4x + 10 = 32x - 24
Step 2: Rearrange
4x + 10 + 24 = 32x
Step 3 Rearrange
10 + 24 = 32x - 4x
Step 4 Simplify
34 = 28x
34/28 = x
x = 1.21 sf
You should now be comfortable with solving equations with brackets and unknowns on both sides.
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