How do you solve #\sqrt { 3x + 4} = \sqrt { 2x + 3}#?

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Answer 1 · 2017-11-06T16:06:40

See a solution process below:

First, square both sides of the equation to eliminate the radicals while keeping the equation balanced:

#(sqrt(3x + 4))^2 = (sqrt(2x + 3))^2#

#3x + 4 = 2x + 3#

Now, subtract #color(red)(4)# and #color(blue)(2x)# from each side of the equation to solve for #x# while keeping the equation balanced:

#-color(blue)(2x) + 3x + 4 - color(red)(4) = -color(blue)(2x) + 2x + 3 - color(red)(4)#

#(-color(blue)(2) + 3)x + 0 = 0 + -1#

#1x = -1#

#x = -1#