Algebraic Expressions to Algebraic Equations

If you are reading all my articles on algebra then you should have gained good understanding of algebraic relations. Also, you know that how they originate from the word phrases in our daily lives.

Algebraic Expressions to Algebraic Equations

In this article I will explain the difference between algebraic expressions and algebraic equations. You will learn that why algebra doesn't stop at algebraic expressions? Why do we need algebraic equations?

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Algebraic Expressions to Algebraic Equations

In my previous articles on algebra, while explaining algebraic relations, I anonymously introduced you with algebraic equations. But, in this article you will find out the clear difference between algebraic expressions and equations.

Algebraic Expressions to Algebraic Equations

Algebraic Expressions to Algebraic Equations

To understand the difference, let's review the following word phrases or sentences;

1. added to 25 times the number of lawns mowed by Arthur.

2. Arthur's earnings are added to 25 times number of lawns mowed by him.

3. Five times a number added to twenty.

4. Five times a number added to twenty is fifty.

Word phrases (sentences) number (1) and (2) are from my previous article. In word phrase number (1), "the added to 25 times number of lawns mowed by Arthur" there is only one variable which is, "number of lawns mowed". Consider we represent this variable by the letter "n"

So, the algebraic relation becomes, "60 + 25n"

In number (2) word phrase, there are two variables, earnings and number of lawns. Represent earnings by letter "e" and number of lawns by letter "n" again. The algebraic relation becomes,

e = 60 + 25n

Notice the difference between both the relations. One of them has equal sign used in it, and we call it an equation instead calling it algebraic expression as "equal" to "equate" and it becomes "equation."

The hint in the word phrase for the equation: The use of words "is" or "are" in word phrases give the indication of equations instead the algebraic expressions.

Now the solution to word phrases number (3) and (4) are given below;

3. Consider the number in the phrase is represented by letter "m", our unknown in the phrase and hence variable. The relation is given as;

5m + 20

No use of words "is" or "are" in the word phrase number (3), therefore no equal sign used in the relation. Hence, the relation is an algebraic expression.

4. In number four the relation is given below;

5m + 20 = 50

As the word "is" used in this word phrase, therefore equal is used in the relation. Hence the relation is an equation.

Equations are like a balance, having both sides equal to one another. Focus your mind to keep the balance of an equation all the times you work on them.

I hope that above explanation is enough to make all my readers understand the difference between algebraic expressions and equations.

In other words, it can be said that when there are variables involved in a relation but no equal sign is used the relation is algebraic expression and if an equal sign is used, the relation is an equation.

From here, we'll take two paths to explore algebra further. One path is exploring equations and the other is exploration of polynomials. So, stay tuned as more algebra is on its way.

Algebraic Expressions to Algebraic Equations