What value will complete the set of equations 15/3x−9 −4=12 and x ≠

Question

_____?
The value that completes the set of equations is x ≠ __

Answer 1

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 \( x \neq 0 \).

Answer 2

0 is wrong

Answer 3

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!

Answer 4

What value of x would cause the fraction 15/3x−9 to be undefined?

Answer 5

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 \( 3 \).