How do you solve the inequality #9>= 4 - 2sqrt( 5x+7)# ?

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Answer 1 · 2016-02-03T05:01:04

Treat the inequality sign like an equal sign.

9 # >= 4 - 2sqrt(5x + 7)#

5 # >=- 2sqrt(5x + 7)#

You will have to switch the in equation sign around since you're dividing by a negative number.

#-5/2 <= sqrt(5x + 7)#

#(-5/2)^2 <= (sqrt(5x + 7))^2#

#25/4 <= 5x + 7#

#25/4 - 28/4 <= 5x#

#-3/4 xx 1/5 <= x#

#-3/20 <= x#

So, your solution is #-3/20 <= x#

Practice Exercises:

a) #sqrt(3x + 6) > 2#

b) #sqrt(3x + 4) + sqrt(8x + 4) <= 10#

Good luck!