1. A number on a card plus 3 is equal to 5. What is the number on the card?
2. Twice of a number minus 4 is equal to the number itself. What is the number?
3.
a. If x represents ‘a number on the card’, write the phrase ‘a number on the card plus 3’ as an algebraic expression using x. Then, formulate (write) the sentence above in (a) as an equation.
b. If x represents the unknown number in (b), write the phrase ‘twice of the number’ as an algebraic expression using x. Then, formulate (write) the sentence above in (b) as an equation.

The following activity that you may work on in groups involves opening problems that will help you to better understand the discussions that follow.

In mathematics, we represent an unknown (a certain number) by a letter, say, x. So, in the above Group Activity, you may formulate the statement in (a) as x + 3 = 5 and the statement in (b) as 2x - 4 = x. Such a letter x that stands in place of the unknown number is called a variable. Moreover, we formally define an equation as follows.

Definition

An equation is a mathematical statement that states two expressions are equal. Two expressions that are required to be equal are separated by the equality symbol, ‘=’

Example

Each of the following are examples of equation.