Question

TEN POINTS:

Given the equation −4 square root of x minus 3 = -12, solve for x and identify if it is an extraneous solution. x = 0, solution is extraneous x = 0, solution is not extraneous x = 12, solution is extraneous x = 12, solution is not extraneous

I think it's D not sure tho.

Answer 1

The equation −4√x - 3 = -12 is solved by isolating the square root, dividing by -4, and then squaring both sides. But the solution found, x = 5.0625, does not match any of the options provided, and without correct options, we cannot confirm if x = 0 or x = 12 are extraneous solutions.

Step-by-step explanation:

To solve the equation −4√x − 3 = −12, first isolate the square root by adding 3 to both sides:

−4√x = −9

Next, divide both sides by −4:

√x = −9 / −4

√x = 2.25

Now square both sides to get rid of the square root:

x = (2.25)2

x = 5.0625

This is not one of the answer choices given, which means there may be a mistake in the options provided or in the initial transcription of the problem. If we look at the answer options, the closest to our computed value of x would be x = 12, option C. However, since this doesn't match our solution, we can't confirm whether x = 0 or x = 12 are extraneous solutions without the correct equation or choices. Typically, we check for extraneous solutions by substituting them back into the original equation.