We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

To solving linear equations inequalities algebra means to find the value or values of the variable used in it.Thus;

(i) to solve the inequality 2x + 4 > 6 means to find the variable x.

(ii) to solve the inequality 5 - 6y $\leq$ 3 means to find the value of y and so on.

The following are the rules must be followed for solving a given linear inequality.

4x + 6 > 7 ⇒ 4x > 7 - 6, 21 $\geq$ 2x + 8 ⇒ 21 - 8 $\geq$ 2x

7x + 4 $\leq$ 18 ⇒ 7x $\leq$ 18 - 4 and so on.

3x - 6 > 5 ⇒ 3x > 5 + 6, 42 $\geq$ 2x - 9 ⇒ 42 + 9 $\geq$ 2x

9x - 1 $\leq$ 20 ⇒ 9x $\leq$ 20 + 1 and so on.

x < y ⇒ px < py and $\left ( \frac{x}{p} \right )$ < $\left ( \frac{x}{p} \right )$

x > y ⇒ px > py and $\left ( \frac{x}{p} \right )$ > $\left ( \frac{x}{p} \right )$

x $\leq$ y ⇒ px $\leq$ py and $\left ( \frac{x}{p} \right )$ $\leq$ $\left ( \frac{x}{p} \right )$

x $\geq$ y ⇒ px $\geq$ py and $\left ( \frac{x}{p} \right )$ $\geq$ $\left ( \frac{x}{p} \right )$

For example x $\leq$ 5 ⇒ 3x $\leq$ 3 x 5 and x $\geq$ 5 ⇒ 3x $\geq$ 3 x 5

Case II : If p is negative,

x < y ⇒ -px > -py and $\left ( \frac{-x}{p} \right )$ > $\left ( \frac{-x}{p} \right )$

x > y ⇒ -px < -py and $\left ( \frac{-x}{p} \right )$ > $\left ( \frac{-x}{p} \right )$

x $\leq$ y ⇒ -px $\geq$ -py and $\left ( \frac{-x}{p} \right )$ $\geq$ $\left ( \frac{-x}{p} \right )$

x $\geq$ y ⇒ -px $\leq$ -py and $\left ( \frac{-x}{p} \right )$ $\leq$ $\left ( \frac{-x}{p} \right )$

(i) x > y $\Leftrightarrow \frac{1}{x}$ < $\frac{1}{y}$ (ii) $x \geq y \Leftrightarrow \frac{1}{x} \leq \frac{1}{y}$

(iii) $x \leq y \Leftrightarrow \frac{1}{x} \geq \frac{1}{y}$ and so on.

11th grade math

From solving linear equations inequalities algebra to Home

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers