Answer:
x = 4
Step-by-step explanation:
[tex] \sqrt{11x + 5} = 7 [/tex]
Square both sides. This step may introduce extraneous solutions, but we will deal with that after we find the solution.
[tex] (\sqrt{11x + 5})^2 = (7)^2 [/tex]
[tex] 11x + 5 = 49 [/tex]
Subtract 5 from both sides.
[tex] 11x = 44 [/tex]
Divide both sides by 11.
[tex] x = 4 [/tex]
Now we check for extraneous solutions. We substitute the value of the solution into the original equation, and we see if it makes the original equation true.
[tex] x = 4 [/tex]
[tex] \sqrt{11x + 5} = 7 [/tex]
[tex] \sqrt{11(4) + 5} = 7 [/tex]
[tex] \sqrt{44 + 5} = 7 [/tex]
[tex] \sqrt{49} = 7 [/tex]
[tex] 7 = 7 [/tex]
7 = 7 is a true equation; therefore, our solution, x = 4, is not an extraneous solution and is the correct solution of the given equation.
Answer: x = 4
