Which of the following is an extraneous solution of square root -3x-2=x+2

Answer:

A) -6

Explanation:

I just took the pretest and got 100%

The extraneous solution of the equation [tex]\(\sqrt{-3x - 2} = x + 2\) is \(x = -6\),[/tex] as it doesn't satisfy the original equation after substitution.

To find the extraneous solutions of the equation [tex]\(\sqrt{-3x - 2} = x + 2\),[/tex] we need to solve the equation and then check each solution to see if it satisfies the original equation.

Given equation: [tex]\(\sqrt{-3x - 2} = x + 2\)[/tex]

Step 1: Square both sides of the equation to eliminate the square root:

[tex](\sqrt{-3x - 2})^2 &= (x + 2)^2 \\[/tex]

[tex]-3x - 2 &= x^2 + 4x + 4[/tex]

Step 2: Rearrange the equation into a quadratic equation:

[tex]0 &= x^2 + 4x + 4 + 3x + 2 \\[/tex]

[tex]0 &= x^2 + 7x + 6[/tex]

Step 3: Solve the quadratic equation by factoring or using the quadratic formula.

The quadratic equation [tex]\(x^2 + 7x + 6 = 0\)[/tex] factors as [tex]\((x + 6)(x + 1) = 0\).[/tex]

So, the solutions are [tex]\(x = -6\) and \(x = -1\).[/tex]

Step 4: Check each solution to see if it satisfies the original equation:

For [tex]\(x = -6\):[/tex]

[tex]\sqrt{-3(-6) - 2} &= (-6) + 2 \\[/tex]

[tex]\sqrt{18 - 2} &= -4 \\[/tex]

[tex]\sqrt{16} &= -4 \\[/tex]

[tex]4 &= -4 \quad (\text{False})[/tex]

For [tex]\(x = -1\):[/tex]

[tex]\sqrt{-3(-1) - 2} &= (-1) + 2 \\[/tex]

[tex]\sqrt{3 - 2} &= 1 \\[/tex]

[tex]\sqrt{1} &= 1 \\[/tex]

[tex]1 &= 1 \quad (\text{True})[/tex]

Step 5: Therefore, the extraneous solution is [tex]\(x = -6\).[/tex]

The probable question may be:

Which of the following is an extraneous solution of [tex]\sqrt{-3x-2} = x+ 2[/tex] ?

x = -6

x = -1

x = 1

x = 6

Avery gets a good interest rate on her car loan.
A. Information utility
B. Form Utility
C. Time utility
D. Possession Utility
E. Place Utility​

Eight times the result of subtracting three from a number is equal to the number increased by 25. What is that number?

After an argument with your parents over whether you should be allowed to stay out until midnight, you are fuming. Your
parents are not persuaded by your arguments, and you begin to think about whether you are being persuasive, and how you
can bolster your position.
Analyze
Evaluate
Question
Reflect

Identify the type of touch.

Chloe hugged her mother goodbye at the front door before heading off to school.
playful
ritual
positive effect
control
task-related

what is my name and also how tall do u think I am