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CBSE Class 11-science Answered

How to split this double inequality into 2 inequations and get the solution set of the system of inequations by intersection method? I didn't understand how to split it into 2 inequations.
Asked by youdhustu | 25 Jun, 2022, 12:10: PM
Expert Answer
To split the double inequality, the middle expression is common. So, it will go with both the inequality.
For exmaple: 3 < 5x - 6 < 9
Here, 5x - 6 is the middle expression which will go wth both the inequalities when separated.
So, 3 < 5x - 6 becomes one inequality and 5x - 6 < 9 becomes the second inequality
Now, for the solution, solve each inequality which we got after splitting the double inequality
Then, take intersection of the values got for the two inequalities
 
If we take the inequality given in the question
negative 11 less or equal than 4 straight x minus 3 space and space 4 straight x minus 3 less or equal than 13 In space the space first space one comma space add space 3 space on space both space sides rightwards double arrow 3 minus 11 less or equal than 4 straight x minus 3 plus 3 rightwards double arrow negative 8 less or equal than 4 straight x rightwards double arrow negative 2 less or equal than straight x space space... space left parenthesis straight I right parenthesis In space the space second space one comma space add space 3 space on space both space sides rightwards double arrow 4 straight x minus 3 plus 3 less or equal than 13 plus 3 rightwards double arrow 4 straight x less or equal than 16 rightwards double arrow straight x less or equal than 4 space space... space left parenthesis II right parenthesis Combining space the space left parenthesis straight I right parenthesis space and space left parenthesis II right parenthesis rightwards double arrow negative 2 less or equal than straight x less or equal than 4 Therefore comma space straight x element of left square bracket negative 2 comma space 4 right square bracket
Answered by Renu Varma | 25 Jun, 2022, 01:40: PM

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