Answer
397.5k+ views
Hint: An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. Here we need to solve for ‘x’ which is a variable. Solving the given inequality is very like solving equations and we do most of the same thing but we must pay attention to the direction of inequality\[( \leqslant , > )\]. We have a simple linear equation type inequality and we can solve this easily.
Complete step by step solution:
Given \[x - 1 > 2\]
We need to solve for ‘x’.
Since we know that the direction of inequality doesn’t change if we add a number on both sides. We add 1 on both sides of the inequality we have,
\[x - 1 + 1 > 2 + 1\]
\[x > 3\]
That is \[x > 3\] is the solution of \[x - 1 > 2\].
We can write it in the interval form. That is \[(3,\infty )\]
Note: If we take a value of ‘x’ in \[(3,\infty )\] and put it in \[x - 1 > 2\], it satisfies. That is
Let put \[x = 4\] in \[x - 1 > 2\],
\[4 - 1 > 2\]
\[3 > 2\]
That is 3 is greater than 2 and it is correct.
We know that \[a \ne b\]says that ‘a’ is not equal to ‘b’. \[a > b\] means that ‘a’ is less than ‘b’. \[a < b\] means that ‘a’ is greater than ‘b’. These two are known as strict inequality. \[a \geqslant b\] means that ‘a’ is less than or equal to ‘b’. \[a \leqslant b\] means that ‘a’ is greater than or equal to ‘b’.
The direction of inequality do not change in these cases:
i) Add or subtract a number from both sides.
ii) Multiply or divide both sides by a positive number.
iii) Simplify a side.
The direction of the inequality change in these cases:
i) Multiply or divide both sides by a negative number.
ii) Swapping left and right hand sides.
Complete step by step solution:
Given \[x - 1 > 2\]
We need to solve for ‘x’.
Since we know that the direction of inequality doesn’t change if we add a number on both sides. We add 1 on both sides of the inequality we have,
\[x - 1 + 1 > 2 + 1\]
\[x > 3\]
That is \[x > 3\] is the solution of \[x - 1 > 2\].
We can write it in the interval form. That is \[(3,\infty )\]
Note: If we take a value of ‘x’ in \[(3,\infty )\] and put it in \[x - 1 > 2\], it satisfies. That is
Let put \[x = 4\] in \[x - 1 > 2\],
\[4 - 1 > 2\]
\[3 > 2\]
That is 3 is greater than 2 and it is correct.
We know that \[a \ne b\]says that ‘a’ is not equal to ‘b’. \[a > b\] means that ‘a’ is less than ‘b’. \[a < b\] means that ‘a’ is greater than ‘b’. These two are known as strict inequality. \[a \geqslant b\] means that ‘a’ is less than or equal to ‘b’. \[a \leqslant b\] means that ‘a’ is greater than or equal to ‘b’.
The direction of inequality do not change in these cases:
i) Add or subtract a number from both sides.
ii) Multiply or divide both sides by a positive number.
iii) Simplify a side.
The direction of the inequality change in these cases:
i) Multiply or divide both sides by a negative number.
ii) Swapping left and right hand sides.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)