How do you calculate equations?

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Many students find solving equations difficult. Corresponding tasks are not only important for school, but also for many professions and in everyday life. Here is a brief overview of how to calculate the variables you are looking for.

Equations are very important for natural sciences.
Equations are very important for natural sciences.

For the quick and error-free solving of Equations you need routine. Practice regularly while you are still having trouble.

How to solve equations with an unknown variable

  • Equations are given in the form that the left and right of an equal sign are each a combination of Counting, Variables and mathematical operands. In equations with an unknown, a variable, which is usually referred to as x, appears one or more times. For example, an equation could be: x / 3 + 20 = 2x + 10.
  • You now have to rearrange the equation so that the variable x is alone on one side. On the other hand, the variable must no longer appear so that you can calculate the value of this side.
  • You rearrange equations by performing individual arithmetic operations, in each case on both the left and right side of the equation. This ensures that both sides of the equation really remain the same.
  • First, check to see if the equation can be simplified. If it contains brackets, it can make sense to multiply them out. Perhaps there are other ways to simplify things, such as adding up individual numbers or expressions. For example, you can combine 2x-3x to -x.
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  • When rearranging equations, you basically have to follow two rules. If you do an addition or subtraction, look at the two sides of the equation in their entirety. For example, if the equation is x + 60 = 6x + 30 and you want to calculate -x, subtract x once on the left and once on the right. The equation is then: 60 = 5x + 30.
  • If you are multiplying or dividing, you are doing this math on each term in the equation separated from the other terms by plus or minus. If you multiply the equation x / 3 + 20 = 2x + 10 by 3, you get x + 60 = 6x + 30. You may understand this procedure better if you imagine putting parentheses on each side of the equation and multiplying or dividing them.
  • So that you can later understand what you have calculated in detail, note the calculation operation carried out in each step behind the equation. It is customary to write the individual steps behind a vertical line.

This is how you calculate x - an example

  1. You should solve the equation x / 3 + 20 = 2x + 10 for x. Simplifications are not possible. To solve the fraction, multiply each term separated by plus or minus by 3. You get: x + 60 = 6x + 30.
  2. Now subtract 30 on both sides. Then the equation is: x + 30 = 6x.
  3. Since you want to put x on one side, do the math -x and you get: 30 = 5x.
  4. Now it is obvious that you need to divide both sides by 5. The solution for x is therefore 6.
  5. Check the solutions to the equations by plugging the found solutions into the output equation.

If you are given a system of equations with two equations and two variables, first rearrange an equation according to one of the variables. Then plug the expression you found for that variable into the other equation and solve for the other variable. The first variable is then calculated with the determined value.

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