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:
\[ { 10 } \]
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 \(x^2 = 18\).
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:
Thus, the two solutions are: \[ x = 3\sqrt{2} \quad \text{and} \quad x = -3\sqrt{2} \]
Now, substituting approximate numerical values:
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!
