Inequalities

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What is inequality in algebra?

In real life, we come across many situations, where things are “not equal”; they may be “greater than” or “less than”.

See examples below:

An inequality is an expression formed using the symbols, <, >, ≤or ≥.

A number line is the best way of showing inequalities. In a number line, let us take a and b are two numbers.

If b > a then b will be to the right of a on the number line. The number which is greater always goes on the right of the number, which is smaller.

Inequalities can always be written in two ways.

For example, we say that 8 is greater than 7, or, 7 is less than 8. In Math, we write 8 > 7 or 7 < 8. In the same way if b > a then a < c using only the ‘greater than’ sign, >.

Example 1:

Write the inequality – $\frac{4}{5}$ < x using only the ‘greater than’ sign, >.

Solution:

– $\frac{4}{5}$ < x can be stated as x > – $\frac{4}{5}$

Sometimes we compare two inequalities; in one like x is greater than 1 and less than 3. Then we write 1 < x > 3.

How do you solve inequalities?

Example 2:

Marlo has a savings of $300 in her account. She wants at least $100 at the end of the month. She withdraws at least $20 every week for miscellaneous expenses like groceries, electric and rent. Write an inequality expression to represent the above situation, if she withdraws $20 for “w” weeks.

Solution: Savings in her account = $300

Withdrawal every week = $20

The inequality expression is 300 – 20w ≥ 100.

Example 3:

What inequality is shown here in this number line?

This number line denotes inequality greater than or equal to 1.

Check Point

State which of the following statements is “True” or “False”.

5 > 9
4 > 7
18 ≥ 4
0.003 < 10 − 5
-3 > -1
A taxi cab charges $1.25 and $0.50 for every km. Neil has just $10 with him. Write an inequality expression which shows Neil’s limits on the budget, assuming the number of kilometers Neil can travel as m.

Which words makes the statement true: is greater than, is less than, is equal to?

15 ____ 213.51
40 ____ 556.48

Which inequality does this number line show?

Answer key

False
False
False
True
False
5m + 1.25 ≤ 10

x < -1

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