Solve equations for x

Don't be afraid of math problems: An equation can easily be solved for the unknown "x". These notes always apply!

What you need:

With this variety Equations You will encounter the unknown "x" for the first time in school mathematics, which you should calculate using an equation.
A simplest example of this kind would be: 3x + 7 = 22. In this equation, the unknown appears only as a simple "x", no square, no root, or something like that ugly.
Such an equation can easily be imagined as a beam balance with two scales that are in equilibrium (due to the actual sign). In our example there are 3 packages of unknown weight x in the left pan, plus 7 kg. There are 22 kg in the right weighing pan. Your task is to find out how much each of these unknown packages weighs.
First, you lose 7 kg on both sides. Mathematically, you do the math - 7 or, to put it casually: The "7" from the left is brought to the right with -7. The new equation then reads: 3x = 22 - 7, i.e. 3x = 15

If 3 packages weigh 15 kg, then 1 package weighs 15: 3 = 5 kg. So you have to divide the equation by "3" on both sides: and you get: x = 5. Actually, it's easy to get here.

Solve equations in brackets - the math expert explains how it works

If there weren't any nasty brackets in the equations - who the rules ...

The case becomes more difficult if the unknown "x" occurs more frequently, here is an example: 7x - 5 = 2x + 8. In this case, the unknown packages are in both the left and right pan.
But even this case can easily be solved by rearranging packages and weights. First, remove 2 unknown packets (2x) from both sides. One obtains: 5x + 5 = 8. And you can then solve this equation as described above: 5x = 3 and x = 3/5 or 0,6
If you have the unknown x in even more complicated cases, you must first order the equation. An example: 7x + 15 - 3x = 8x - 1 + 2x - 17. Here, the left and right sides are combined as far as possible, i.e. the unknowns and the Counting. You get: 4x + 15 = 10x - 18. You already know this case.
It gets "worse" when parentheses appear. Here is an example: 2 (x + 1) = 15x - 3 (x-2). The same applies here: keep calm and work according to a scheme: 1. Dissolve brackets, 2. Summarize numbers and unknowns on the left and right, 3. solve the equation as above.
Dissolve brackets: 2x + 2 = 15x - 3x + 6 (pay attention to the signs in front of the brackets, the result is +6!)
To summarize: 2x +2 = 12 x + 6
Solve the equation: -10x + 2 = 6 (remove 12x on both sides!), Then -10x = 4 (remove 2), then x = 4: (-10) = -0.4 (pay attention to the sign!) .
When the system is clear, practice helps! Because understanding does not mean that you will immediately master it perfectly.

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