An  equation is an equality between two algebraic expressions that gives us information about the value of the unknown involved in them. A linear equation an equation in which the unknown is not raised to any power greater than 1. For this reason, they are also called first-grade equations.

Example: 2x+1=0.

  • This equation indicates that the value of x meets the following: if we multiply it by 2 and add 1, the result must be equal to 0. From here it follows that 2x=-1.
  • Since twice x is equal to -1, x It has to be half of -1, that is: x=-1/2, thus solving the equation.

What we just did is sometimes understood as the “balance rule”: If we imagine that both sides of the equation are two plates of a scale in equilibrium, we have to do exactly the same on both sides to keep the balance. To solve '2x+1=0' we would do the following:

  • To start, we subtract 1 from both sides of the equation, converting '2x+1=0' to '2x=-1'.
  • Lastly, we divide by 2 on both sides of the equation and '2x=-1' becomes 'x=-1/2'.

The way to understand these procedures is through the “rules of the pass”: what is adding happens by subtracting (and vice versa), what is multiplying happens dividing (and vice versa). The solution of the equation would then be done as follows:

  • In the first part, the 1 that is adding in '2x+1=0' goes by subtracting to the other side of the equal: '2x=-1'.
  • Finally, the 2 that is multiplying goes through dividing and we get 'x=-1/2'.

Last modified: Friday, 19 July 2024, 2:56 PM