Given the equation sqrt(x+1)+3=0, explain how to and solve this equation. Is the solution extraneous? Explain​

√(x + 1) + 3 = 0   ==>   √(x + 1) = -3

has no real solutions, since the square root cannot be a negative number. But if we were to ignore that for the moment, one might try taking the square of both sides, which gives

(√(x + 1))² = (-3)²   ==>   x + 1 = 9   ==>   x = 8

But this is not a valid solution, since

√(8 + 1) = √9 = 3 ≠ -3

While -3 is a square root of 9, we had started off with the *positive* square root of x + 1.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

the answer is d

step-by-step explanation: