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 | 25th 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 | 25th Jun, 2022, 01:40: PM