How to solve first degree equations?

There are lots of methods to solve equations. The choice of the right method generally depends on the degree of the equation; this is, on the exponent of the unknown quantity. The simplest equations are the first degree ones. The higher is the degree of the equation, the more complex it becomes.

Could you give an example?

Let’s suppose that we want to solve the problem suggested by the following picture:

The aim is to find the weight of those boxes. Let’s start by stating the problem which will have a first degree equation and the unknown quantity `x` stands for the weight of one of the boxes (the solution is possible only if all the boxes have the same weight). On the left plate of the balance we have `2x + 500 + 100` and on the right plate we have `x + 250 + 500`. Having in mind this is a first degree equation, the most common method is trying to isolate the unknown quantity within the first member and then we will find its value. We have to stress that in the case of the balance we can add to or take from the plates the same weight and they will keep the balance. According to the analogy, in an equation we can add or subtract both members by a constant and we will always get an equivalent equation. Here it is the solution (abbreviated):

`2x + 500 + 100 = x + 250 + 500 hArr`
`hArr 2x - x = 250 + 500 - 500 - 100 hArr`
`hArr x = 150`

So, the weight of each one of those boxes is 150 grams.

The practical rule in these cases consists of taking care about changing the operation every time a number goes from one member to another. For instance, if a number is added in the second member it goes to the first member but it will be subtracted and if a number is multiplied in the first member it will be divided in the second one.

May I practice?

Having in mind what has previously been explained; try to see if you are able to find the weight of each box in the following balance. At the end do not forget to try your answer to know if it is right!

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