Question

Sehyr solved the equation w2−7=11. She seems to have made an error in her work because the solution she found does not work.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To verify if Sehyr made an error, let's solve the equation w^2 - 7 = 11.

Adding 7 to both sides of the equation, we get:
w^2 = 18

Taking the square root of both sides, we have:
w = ±√18

Simplifying the square root of 18, we get:
w ≈ ±4.242641

Therefore, the solutions to the equation are approximately w ≈ 4.242641 and w ≈ -4.242641.

If Sehyr found a different solution that does not match the solutions above, then she made an error in her work.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To verify if Sehyr made an error in her work, let's solve the equation step-by-step:

Given equation: w^2 - 7 = 11

Step 1: Add 7 to both sides of the equation to isolate the w^2 term.
w^2 - 7 + 7 = 11 + 7
w^2 = 18

Step 2: Take the square root of both sides to solve for w.
√w^2 = √18
w = ±√18
w ≈ ±4.2426

Step 3: Substitute the value of w into the original equation to check if it satisfies the equation.

When w = 4.2426:
w^2 - 7 = 11
(4.2426)^2 - 7 = 11
18 - 7 = 11
11 = 11

Since the equation is satisfied when w = 4.2426, this is a valid solution.

However, Sehyr mentioned that the solution found does not work. Therefore, there might have been an error in her calculations or statement.

Answer 3

[AI-generated answer — Explain Bot]

To find out if Sehyr made an error in solving the equation w^2 - 7 = 11, let's first examine her solution and then check if it satisfies the original equation.

Sehyr's solution may involve simplifying the equation and then finding the value of w. Let's assume that Sehyr's solution is as follows:

w^2 - 7 = 11

Step 1: Add 7 to both sides of the equation:

w^2 = 11 + 7
w^2 = 18

Step 2: Take the square root of both sides of the equation:

√w^2 = √18
w = ±√18

This is most likely where Sehyr made the error. Taking the square root of 18 yields two possible values: √18 and -√18. However, while these are the correct solutions to the equation, neither of them satisfies the original equation w^2 - 7 = 11.

To verify this, substitute both values of w back into the original equation:

For w = √18:
√18^2 - 7 = 11
18 - 7 = 11
11 = 11

For w = -√18:
(-√18)^2 - 7 = 11
18 - 7 = 11
11 ≠ 11

As shown, only the value w = √18 satisfies the original equation, while w = -√18 does not. Therefore, it seems that Sehyr made an error in her work since her solution does not satisfy the original equation.