How do you solve #sqrt(x+1)+2=4# and check the solution?

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Answer 1 · 2017-06-23T17:35:14

x = 3

1. Subtract 2 from both sides to isolate the square root.

#sqrt(x+1) + 2 - 2 = 4 - 2#
#sqrt(x+1) = 2#

2. To get rid of the square root, square both sides.

#(sqrt(x+1))^2 = 2^2#
#x + 1 = 4#

3. Subtract 1 from both sides to find x.

#x + 1 - 1 = 4 - 1#
#x = 3#

Now that we know that x = 3, check the solution by plugging its value back into the original equation.

#sqrt(3 + 1) + 2 = 4#
#sqrt(4) + 2 = 4#
#2 + 2 = 4#
#4 = 4#

The solution, x = 3, works!