Asked by kacey
What value will complete the set of equations 15/3x−9 −4=12 and x ≠
_____?
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
To solve the equation \( \frac{15}{3x} - 9 - 4 = 12 \), we will first simplify and rearrange the equation.
1. **Combine terms on the left side**:
\[
\frac{15}{3x} - 13 = 12
\]
2. **Add 13 to both sides**:
\[
\frac{15}{3x} = 12 + 13
\]
\[
\frac{15}{3x} = 25
\]
3. **Multiply both sides of the equation by \( 3x \)**:
\[
15 = 25 \cdot 3x
\]
\[
15 = 75x
\]
4. **Divide both sides by 75**:
\[
x = \frac{15}{75}
\]
\[
x = \frac{1}{5}
\]
Now, we need to consider the condition \( x \neq \ldots \).
Since \( 3x \) cannot be zero (as it would make the denominator zero in the original equation), we find:
\[
3x \neq 0 \implies x \neq 0
\]
Thus, the value that completes the set of equations is:
\[
x \neq 0
\]
In conclusion, the complete statement is:
The value that completes the set of equations is \( x \neq 0 \).
1. **Combine terms on the left side**:
\[
\frac{15}{3x} - 13 = 12
\]
2. **Add 13 to both sides**:
\[
\frac{15}{3x} = 12 + 13
\]
\[
\frac{15}{3x} = 25
\]
3. **Multiply both sides of the equation by \( 3x \)**:
\[
15 = 25 \cdot 3x
\]
\[
15 = 75x
\]
4. **Divide both sides by 75**:
\[
x = \frac{15}{75}
\]
\[
x = \frac{1}{5}
\]
Now, we need to consider the condition \( x \neq \ldots \).
Since \( 3x \) cannot be zero (as it would make the denominator zero in the original equation), we find:
\[
3x \neq 0 \implies x \neq 0
\]
Thus, the value that completes the set of equations is:
\[
x \neq 0
\]
In conclusion, the complete statement is:
The value that completes the set of equations is \( x \neq 0 \).
Answered by
GPT-4o mini
Let's reconsider the original equation and the requirement for \( x \) to clarify what values it specifically cannot take.
The original equation is:
\[
\frac{15}{3x} - 9 - 4 = 12
\]
**Step 1: Simplify the equation.**
Combine the terms on the left side:
\[
\frac{15}{3x} - 13 = 12
\]
Add \( 13 \) to both sides:
\[
\frac{15}{3x} = 25
\]
**Step 2: Solve for \( x \).**
Multiply both sides by \( 3x \):
\[
15 = 25 \cdot 3x
\]
This can be rewritten as:
\[
15 = 75x
\]
To find \( x \), we can divide both sides by \( 75 \):
\[
x = \frac{15}{75} = \frac{1}{5}
\]
**Step 3: Determine the restrictions on \( x \).**
The original equation includes a fraction, which implies that the denominator cannot be zero:
From \( 3x \) in the denominator, we must have:
\[
3x \neq 0 \implies x \neq 0
\]
Therefore, the value that completes the set of equations is:
\[
x \neq 0
\]
This is correct—is there a specific value or condition you were expecting other than this? If you have any other constraints in mind or would like to clarify further, please let me know!
The original equation is:
\[
\frac{15}{3x} - 9 - 4 = 12
\]
**Step 1: Simplify the equation.**
Combine the terms on the left side:
\[
\frac{15}{3x} - 13 = 12
\]
Add \( 13 \) to both sides:
\[
\frac{15}{3x} = 25
\]
**Step 2: Solve for \( x \).**
Multiply both sides by \( 3x \):
\[
15 = 25 \cdot 3x
\]
This can be rewritten as:
\[
15 = 75x
\]
To find \( x \), we can divide both sides by \( 75 \):
\[
x = \frac{15}{75} = \frac{1}{5}
\]
**Step 3: Determine the restrictions on \( x \).**
The original equation includes a fraction, which implies that the denominator cannot be zero:
From \( 3x \) in the denominator, we must have:
\[
3x \neq 0 \implies x \neq 0
\]
Therefore, the value that completes the set of equations is:
\[
x \neq 0
\]
This is correct—is there a specific value or condition you were expecting other than this? If you have any other constraints in mind or would like to clarify further, please let me know!
Answered by
GPT-4o mini
The expression \( \frac{15}{3x - 9} \) will be undefined when the denominator is equal to zero. To find the value of \( x \) that causes this, we set the denominator equal to zero and solve for \( x \):
\[
3x - 9 = 0
\]
**Step 1: Solve for \( x \)**
Add \( 9 \) to both sides:
\[
3x = 9
\]
Now, divide both sides by \( 3 \):
\[
x = \frac{9}{3} = 3
\]
**Conclusion:**
The value of \( x \) that would cause the fraction \( \frac{15}{3x - 9} \) to be undefined is:
\[
x = 3
\]
This means the fraction is undefined when \( x \) is equal to \( 3 \).
\[
3x - 9 = 0
\]
**Step 1: Solve for \( x \)**
Add \( 9 \) to both sides:
\[
3x = 9
\]
Now, divide both sides by \( 3 \):
\[
x = \frac{9}{3} = 3
\]
**Conclusion:**
The value of \( x \) that would cause the fraction \( \frac{15}{3x - 9} \) to be undefined is:
\[
x = 3
\]
This means the fraction is undefined when \( x \) is equal to \( 3 \).