Question

Solve each equation, showing all steps leading to your answer. Then check your answer to determine if any of the solutions are extraneous

1.
x+1−−−−−√+5=x


2.
5x−−√−x=0


3.
2x+1−−−−−√+1=x


4.
3x−2−−−−−√+3=4x

Answer 1

\[\sqrt{x+1}+5=x\]

\[\sqrt{5x}-x=0\]

\[\sqrt{2x+1}+1=x\]

\[\sqrt{3x-2+3=4x}\]

Here are the equations

Answer 2

i'll do the first one
others are similar
\[\sqrt{x+1}+5=x\] subtract \(5\)
\[\sqrt{x+1}=x-5\] square both sides (correctly)
\[x+1=(x-5)^2\]
\[x+1=x^2-10x+25\] solve the quadratic equation by setting it equal to zero and factoring
\[x^2-11x+24=0\]
\[(x-3)(x-8)=0\] set the factors equal to zero and get \[x-3=0\iff x=3\] or
\[x-8=0\iff x=8\] then check the answer in the original equation

Answer 3

Thank you!

Answer 4

\[\sqrt{3+1}+5=3\]
\[\sqrt{4}+5=3\]
\[2+5=3\] no not true \(3\) is not a solution
\[\sqrt{8+1}+5=8\]
\[\sqrt{9}+5=8\]
\[3+5=8\] true, \(8\) is a solution

Answer 5

Thanks! I appreciate it a lot!!

Answer 6

yw