Question

Use set notation to express the value(s) that make the equation $2x = 20$ true. Enter your response using set notation.

Answer 1

Both −6 and 6 make the equation x22=18 true. Use set notation to express these solutions. When entering your response, list elements in the set from least to greatest, with a comma between each element in the set.

Answer 2

Remember to include all the values that make the equation true within the set. List the elements of the set from least to greatest, with a comma between each element in the set.

Answer 3

To solve the equation \(2x = 20\), we first isolate \(x\) by dividing both sides of the equation by 2:

\[
x = \frac{20}{2} = 10
\]

Thus, the solution to the equation is \(x = 10\).

In set notation, we express the solution as:

\[
\{ 10 \}
\]

Therefore, the final answer in set notation is:

\[
\{ 10 \}
\]

Answer 4

To solve the equation \( x^2 = 18 \), we can take the square root of both sides. This gives us:

\[
x = \sqrt{18} \quad \text{or} \quad x = -\sqrt{18}
\]

Since \( \sqrt{18} = 3\sqrt{2} \), we can express the two solutions as:

\[
x = 3\sqrt{2} \quad \text{and} \quad x = -3\sqrt{2}
\]

The approximate numerical values of these solutions are \( 3\sqrt{2} \approx 4.24 \) and \( -3\sqrt{2} \approx -4.24 \).

However, you mentioned that both \(-6\) and \(6\) make the equation true. Let's verify:

Substituting \(x = 6\):
\[
6^2 = 36 \quad \text{(not true for } x^2 = 18 \text{)}
\]

Substituting \(x = -6\):
\[
(-6)^2 = 36 \quad \text{(also not true for } x^2 = 18 \text{)}
\]

So it appears there might be a misunderstanding about the solutions to the equation based on your prompt.

The actual solutions for \(x^2 = 18\) are:
\[
\{-3\sqrt{2}, 3\sqrt{2}\}
\]

In numeric terms, approximating \(3\sqrt{2} \approx 4.24\) and \( -3\sqrt{2} \approx -4.24\), we present the solutions in increasing order. The final answer for the solutions in set notation is:

\[
\{-3\sqrt{2}, 3\sqrt{2}\}
\]

If we want to list them in decimal approximations from least to greatest, we would represent it as:

\[
\{-4.24, 4.24\}
\]

However, since you initially mentioned \(-6\) and \(6\) (which do not satisfy \(x^2 = 18\)), if you're still interested in writing those numbers in set notation, the correct context is:

\[
\{-6, 6\}
\]

Just be aware that these do not satisfy the original equation \(x^2 = 18\).

Answer 5

Apologies for the confusion in my previous messages. Let's clarify the original equation you mentioned:

The equation is \(x^2 = 18\).

The solutions to this equation can be determined as follows:

1. Taking square roots, we obtain:
\[
x = \sqrt{18} \quad \text{or} \quad x = -\sqrt{18}
\]
2. The square root of 18 can be simplified:
\[
\sqrt{18} = 3\sqrt{2}
\]

Thus, the two solutions are:
\[
x = 3\sqrt{2} \quad \text{and} \quad x = -3\sqrt{2}
\]

Now, substituting approximate numerical values:
- \(3\sqrt{2} \approx 4.24\)
- \(-3\sqrt{2} \approx -4.24\)

List the solutions in set notation from least to greatest:

Approximately, we have:

\[
\{-3\sqrt{2}, 3\sqrt{2}\}
\]

If we use numerical approximations for clarity, the set of solutions is:

\[
\{-4.24, 4.24\}
\]

However, **if you require the numeric values you mentioned earlier**, we can consider all unique solutions including \(-6\) and \(6\), but note they do not satisfy \(x^2 = 18\).

Thus, if we follow your instruction to list values based on your last indication and include \(-6\) and \(6\) as mentioned, the final response in set notation listing them from least to greatest with commas in between would be:

\[
\{-6, 6\}
\]

If the strict mathematical context is maintained, the solutions to the equation \(x^2 = 18\) are:

\[
\{-3\sqrt{2}, 3\sqrt{2}\} \quad \text{or numerically} \quad \{-4.24, 4.24\}
\]

Please let me know if you need any further clarification!