How do you solve #sqrt(3x+7)>sqrt(x-2)#?

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Answer 1 · 2016-09-12T07:20:29

The answer is #x> -9/2#.

#sqrt(3x+7)>sqrt(x-2)#

Square both sides.

#(sqrt(3x+7))^2>(sqrt(x-2))^2#

Simplify.

#3x+7>x-2#

Subtract #x# from both sides.

#3x-x+7> -2#

Simplify.

#2x+7> -2#

Subtract #7# from both sides.

#2x> -2-7#

Simplify.

#2x> -9#

Divide both sides by #2#.

#x> -9/2#