Linear Inequation in One Variable

We will discuss here about the linear inequation in one variable.


The mathematical statement which says that one quantity is not equal to another quantity is called an inequation.

For example: If m and n are two quantities such that m ≠ n; then any one of the following relations (conditions) will be true:

i.e., either (i) m > n

(ii) m ≥ n

(iii) m < n

Or, m ≤ n

Each of the four conditions, given above, is an inequation.




Consider the following statement:

“x is a number which when added to 2 gives a sum less than 6.”

The above sentence can be expressed as x + 2 < 6, where ‘<’ stands for “is less than”.

x + 2 < 6 is a linear inequation in one variable, x.

Clearly, any number less than 4 when added to 2 has a sum less than 6.

So, x is less than 4.

We say that the solutions of the inequation x + 2 < 6 are x < 4.

The form of a linear inequation in one variable is ax + b < c, where a, b and c are fixed numbers belonging to the set R.

If a, b and c are real numbers, then each of the following is called a linear inequation in one variable:

Similarly, ax + b > c             (‘>’ stands for “is greater than”)

ax + b ≥ c                           (‘≥’ stands for “is greater than or equal to”)

ax + b ≤ c                           (‘≤’ stands for “is less than or equal to”)

are linear inequation in one variable.

In an inequation, the signs ‘>’, ‘<’, ‘≥’ and ‘≤’ are called signs of inequality.


Let m and n be any two real numbers, then

1. m is less than n, written as m < n, if and only if n – m is positive. For example,

(i) 3 < 5, since 5 – 3 = 2 which is positive.

(ii) -5 < -2, since -2 – (- 5) = -2 + 5 = 3 which is positive.

(iii) \(\frac{2}{3}\) < \(\frac{4}{5}\), \(\frac{4}{5}\) – \(\frac{2}{3}\) = \(\frac{2}{15}\) which is positive.


2. m is less than or equal to n, written as m ≤ n, if and only if n – m is either positive or zero. For example,

(i) -4 ≤ 7, since 7 – (-4) = 7 + 4 = 11 which is positive.

(ii) \(\frac{5}{8}\) ≤ \(\frac{5}{8}\), since \(\frac{5}{8}\) - \(\frac{5}{8}\) = 0.


3. m is greater than or equal to n, written as m ≥ n, if and only if m – n is either positive or zero. For example,

(i) 4 ≥ -6, since 4 – (-6) = 4 + 6 = 10 which is positive.

(ii) \(\frac{5}{8}\) ≥ \(\frac{5}{8}\), since \(\frac{5}{8}\) – \(\frac{5}{8}\) = 0.


4. m is greater than n, written as m > n, if and only if m – n is positive. For example,

(i) 5 > 3, since 5 – 3 = 2 which is positive.

(ii) -8 > -12, since -8 – (- 12) = -8 + 12 = 4 which is positive.

(iii) \(\frac{4}{5}\) > \(\frac{2}{3}\), since \(\frac{4}{5}\) – \(\frac{2}{3}\) = \(\frac{2}{15}\) which is positive.






10th Grade Math

From Linear Inequation in One Variable to HOME


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.



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.



Share this page: What’s this?

Recent Articles

  1. Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

    Mar 28, 24 06:33 PM

    Multiplying by 3-Digit Number
    In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

    Read More

  2. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  3. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  4. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  5. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Mar 25, 24 04:18 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More