# 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

### Answered by Renu Varma | 25th Jun, 2022, 01:40: PM

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