Eduki

Equation

When two expressions are placed side by side separated by an equal sign, then it is called an equation. For example, 2+3=5 is a numerical equation.

On the other hand, 3+7=9 is also an equation; it is not true that is another subject matter but nonetheless, it is an equation. It is a false equation. 

𝑥+2=5 is another type of equation. Here only one type of variable “x” has been used so it is a one-variable equation.

Laws of Equality

As discussed, while defining variables, it only arises when we need a placeholder for some quantity without a definitive value. The equation is interpreted as some number when increased by 2 becomes equal to 5. Solving an equation means finding the appropriate value of the variable which when substituted into the equation will satisfy both sides of the equation. To find out the number that increased by 2 makes 5, it would be common sense to decrease 2 from both sides so that the value of the variable gets revealed.

𝑥+2=5

or, 𝑥+2-2=5-2

or, 𝑥=3

The process applied here is associated with the additive property of equality which suggests that when a particular equal quantity is added/reduced from two equal quantities, then the resulting quantities are also equal. 

Another property of equality commonly used is the multiplicative property of equality in which a particular quantity is multiplied or divided by on both sides of the equation.

For example, 𝑥/5=20

Multiplying both sides by 5

(𝑥/5) x 5 =20 x 5

𝑥=100

Using multiplicative law of equality

Suppose that there is a picnic being planned for a class in a school. It is found that 500 dollars are required for a class of 25 people. Then what will be the share of each student that needs to be collected?

If we want to find out the answer, we have to divide 500 into 25 equal portions such that there is an equal load on all the students. In other words, it can also be said that some quantity that is added 25 times makes 500. Or what multiplied by 25 makes 500. If 𝑥 denotes the share of each student, then

25 times 𝑥 =500

25𝑥=500

25*𝑥= 25*20

That is 𝑥=20

Each student has to contribute 20 dollars to the cause in order to make the total collection to be 500 dollars.

A variable will always be representing some kind of quantity according to its context. That quantity may be completely unknown or any number of a specified set suitable to the context. For example, if 4r is an expression used to denote the profit earned by selling “r” t-shirts when the profit rate per t-shirt is 4 dollars then r can have any value but not a negative number because a negative number of t-shirts won't make any sense.