30-01-2015
Mathematics

Answered

For which value of a are all the solutions of 2(x-5)>3x+a less than or equal 5?

Answer :

31-01-2015

[tex]2(x-5)>3x+a \\ 2x-10 > 3x+a \\ 2x-3x>a+10 \\ -x>a+10 \ \ \ |\times (-1) \\ x<-a-10[/tex]

The solutions must be less than or equal to 5.
[tex]-a-10 \leq 5 \\ -a \leq 5+10 \\ -a \leq 15 \ \ \ |\times (-1) \\ a \geq -15[/tex]

All the solutions are less than or equal to 5 for a≥-15.

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