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

5 answers

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:

\[ { 10 } \]

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.

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 \(x^2 = 18\).

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.

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!