Question
What value will complete the set of equations 15/3x−9−4=12 and x≠_____?(1 point)
The value that completes the set of equations is x≠__
The value that completes the set of equations is x≠__
Answers
Answered by
GPT-4o mini
Let's first solve the equation \( \frac{15}{3}x - 9 - 4 = 12 \).
1. Simplify the fraction:
\[
\frac{15}{3} = 5
\]
So the equation becomes:
\[
5x - 9 - 4 = 12
\]
2. Combine like terms:
\[
5x - 13 = 12
\]
3. Add 13 to both sides:
\[
5x = 25
\]
4. Divide both sides by 5:
\[
x = 5
\]
Now, from the problem statement "x ≠ _____", we need to determine any restrictions on \( x \).
Since there are no denominators or square roots in the original equation that could lead to undefined values, the only value that we have found is \( x = 5 \).
Thus, the value that completes the set of equations is:
\[
x \neq 5
\]
Final answer:
The value that completes the set of equations is \( x \neq 5 \).
1. Simplify the fraction:
\[
\frac{15}{3} = 5
\]
So the equation becomes:
\[
5x - 9 - 4 = 12
\]
2. Combine like terms:
\[
5x - 13 = 12
\]
3. Add 13 to both sides:
\[
5x = 25
\]
4. Divide both sides by 5:
\[
x = 5
\]
Now, from the problem statement "x ≠ _____", we need to determine any restrictions on \( x \).
Since there are no denominators or square roots in the original equation that could lead to undefined values, the only value that we have found is \( x = 5 \).
Thus, the value that completes the set of equations is:
\[
x \neq 5
\]
Final answer:
The value that completes the set of equations is \( x \neq 5 \).
Answer
wrong
Answered by
GPT-4o mini
Let's carefully solve the equation again and identify any restrictions on \( x \).
Given the equation:
\[
\frac{15}{3}x - 9 - 4 = 12
\]
1. First, simplify \( \frac{15}{3} \):
\[
\frac{15}{3} = 5
\]
This gives us:
\[
5x - 9 - 4 = 12
\]
2. Next, combine the constants \( -9 \) and \( -4 \):
\[
5x - 13 = 12
\]
3. Add 13 to both sides:
\[
5x = 25
\]
4. Now, divide by 5:
\[
x = 5
\]
Now, we check for any restrictions on \( x \). Since there are no operations in the equation that result in division by zero or other exclusions, we don’t have any additional restrictions from the equation itself.
To conclude, \( x \neq 5 \) is the only value to be excluded based on our previous calculations, which indicates that when solving for \( x \), it leads directly to \( x = 5 \). The notation \( x \neq \) implies this is the value at which we'd have an issue (i.e., we don’t want to take that solution as valid since our equation outputs that value).
Thus, the corrected answer remains:
\[
x \neq 5
\]
If you were expecting a different context or error, please let me know, and I can provide additional clarification!
Given the equation:
\[
\frac{15}{3}x - 9 - 4 = 12
\]
1. First, simplify \( \frac{15}{3} \):
\[
\frac{15}{3} = 5
\]
This gives us:
\[
5x - 9 - 4 = 12
\]
2. Next, combine the constants \( -9 \) and \( -4 \):
\[
5x - 13 = 12
\]
3. Add 13 to both sides:
\[
5x = 25
\]
4. Now, divide by 5:
\[
x = 5
\]
Now, we check for any restrictions on \( x \). Since there are no operations in the equation that result in division by zero or other exclusions, we don’t have any additional restrictions from the equation itself.
To conclude, \( x \neq 5 \) is the only value to be excluded based on our previous calculations, which indicates that when solving for \( x \), it leads directly to \( x = 5 \). The notation \( x \neq \) implies this is the value at which we'd have an issue (i.e., we don’t want to take that solution as valid since our equation outputs that value).
Thus, the corrected answer remains:
\[
x \neq 5
\]
If you were expecting a different context or error, please let me know, and I can provide additional clarification!