Why?
Task 1. The depth of water beside a dock is 80 cm. One third of a vertical pole sank onto bottom mud and two fifth was above water level. How high is the pole?
Task 2. There were benches for guests on a summer event. All rows had equal number of benches. If there were 12 persons in one row, 32 guests had no seat. If there were 13 persons in a row, only 9 persons were without a seat. How many guests were there in this event?
Both of these tasks require an unknown in an equation in order to find a solution. Different kind of equations are needed in engineering tasks all the time.
How?
Equation means equality for two expressions.
For example, consider the following equation:
In the middle, we have the equals sign (). The expression , which is located on the left side of the equals sign, is called the left-hand side of the equation. Similarly, the expression , which is located on the right side of the equals sign, is called the right-hand side of the equation. The symbol is called a variable (or unknown).
Our objective is to solve the equation, that is, find a value or expression for the variable so that the left-hand side and the right-hand side are equal. For example, in the above equation, we notice that the value of 1 for (we denote this ) is the solution of the equation: for the left-hand side, we would get , and similarly for the right-hand side, we would get . Thus, we say that the solution satisfies the equation.
An equation is equivalent with the original equation (meaning the equations have identical solutions), if
- the same number is added for both sides of the equation,
- the same number is subtracted from both sides of the equation,
- both sides are multiplied or divided with the same number which is NOT zero.
- the left-hand side and the right-hand side are swapped.
