Question

Algebra 2 question. Gives 100 points. Please help.

Answer 1

x = 4

Explanation:

`√(11x + 5) = 7`

Square both sides. This step may introduce extraneous solutions, but we will deal with that after we find the solution.

`(√(11x + 5))^2 = (7)^2`

`11x + 5 = 49`

Subtract 5 from both sides.

`11x = 44`

Divide both sides by 11.

`x = 4`

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.

`x = 4`

`√(11x + 5) = 7`

`√(11(4) + 5) = 7`

`√(44 + 5) = 7`

`√(49) = 7`

`7 = 7`

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