Linear Equation in One Variable

Before going to the actual topic, i.e, linear equation in one variable, let me introduce you to the basics. Basically there are two thing in mathematics, namely, expression and another thing ‘equation’. An algebraic expression is a mathematical phrase that can contain numerics, variables and operators such as +, -, *, /. For example, 3x + 9 is a mathematical expression.

Now coming to equations, equations are similar to expression except for that equations contain ‘equal to’ operator with some other expressions. Thus, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. Variables are the unknown part of an equation or expression. For example, 4x + 15 = 20 is an equation in one variable, while 3x + 4y = 15 is an equation in two variables i.e., ‘x’ and ‘y’.

Now moving onto the actual topic, linear equation is an equation that gives a straight line when plotted on a graph. Linear equation in one variable is an equation with one unknown quantity which when plotted on the graph gives a straight line.

Definition: If an equation involves only one variable and the highest index of power of that variable is 1, the equation is called a linear equation in one variable.


Following are some examples of linear equation in one variable:

(i) 2x = 8

(ii) 4y = 9

(iii) 3z = 7

(iv) 2x + 4= 7

(v) 81x + 45 =123

All the above mentioned examples have only one variable and are linear in nature. So, they are known as linear equation in one variable.

The equation x2 = 7x + 5 is not a linear equation because the highest index of power of the variable x in it is 2.

Again, x + 5y = 10 is a linear equation in two variables x, y but not in one variable, x or y.

The general form of a linear equation in one variable x is ax + b = 0, a ≠ 0 or px = q, p ≠ 0.


Framing linear equation in one variable from given word problem:

Steps involved in framing of linear equation in one variable from the given word problem are as follows:

Step I: first of all read the given problem carefully and note down the given and required quantities separately.

Step II: Denote the unknown quantities as ‘x’, ‘y’, ‘z’, etc.

Step III: Then translate the problem into mathematical language or statement.

Step IV: Form the linear equation in one variable using the given conditions in the problem.

Sep V: Solve the equation for the unknown quantity.


Now let us try to form some linear equations from given problems.

1. The sum of two numbers is 25, one of the numbers is twice the other. Find the numbers.

Solution:

Let one of the number be ‘x’.

It is given that 2nd number is two times the first number. so 2nd number = 2x.

Now sum of two numbers = 25.

Now when we convert the statement into mathematical statement, then the equation becomes, x + 2x = 25. So, 3x = 25 is our required linear equation in one variable.


2. The difference between two numbers is 70. If the numbers are in ratio 3:5. Then, find the numbers.

Solution:

Let the common ratio be ‘x’.

The 1st number = 3x and 2nd number = 5x.

Now it is given that the difference between them is 70. So, converting the statement into mathematical statement we get,

5x – 3x = 70, i.e., 2x = 70 is our required linear equation in one variable.


All other word problems can be converted into mathematical statement or linear equations using above mentioned steps.





9th Grade Math

From Linear Equation in One Variable to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheets on Comparison of Numbers | Find the Greatest Number

    Oct 10, 24 05:15 PM

    Comparison of Two Numbers
    In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging…

    Read More

  2. Counting Before, After and Between Numbers up to 10 | Number Counting

    Oct 10, 24 10:06 AM

    Before After Between
    Counting before, after and between numbers up to 10 improves the child’s counting skills.

    Read More

  3. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Oct 10, 24 03:19 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  4. Place Value | Place, Place Value and Face Value | Grouping the Digits

    Oct 09, 24 05:16 PM

    Place Value of 3-Digit Numbers
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More

  5. 3-digit Numbers on an Abacus | Learning Three Digit Numbers | Math

    Oct 08, 24 10:53 AM

    3-Digit Numbers on an Abacus
    We already know about hundreds, tens and ones. Now let us learn how to represent 3-digit numbers on an abacus. We know, an abacus is a tool or a toy for counting. An abacus which has three rods.

    Read More