Question

Rewrite the equation 52x−8−1=9 as two equations joined by “and.”(1 point)
Responses

52x−8=9 and x≠−8
Start Fraction 5 over 2 x minus 8 End Fraction equals 9 and x does not equal negative 8

52x−8−1=9 and x≠8
Start Fraction 5 over 2 x minus 8 End Fraction minus 1 equals 9 and x does not equal 8

52x−8−1=9 and x≠4
Start Fraction 5 over 2 x minus 8 End Fraction minus 1 equals 9 and x does not equal 4

52x−8−1=9 and x≠−4

Answer 1

To rewrite the equation \( 52x - 8 - 1 = 9 \) as two equations joined by "and," we first simplify the original equation:

1. Combine like terms on the left side:
\[ 52x - 9 = 9 \]

2. Now, we can rewrite this equation as:
\[ 52x - 9 = 9 \quad \text{and} \quad x \neq \text{a specific value} \]

The specific value that would make the equation undefined would typically come from constraints within the context of the problem, but straightforwardly solving this equation gives us:

\[
52x - 9 = 9 \quad \text{and} \quad x \neq \text{undefined value}
\]

If we solve \(52x - 9 = 9\) for \(x\):
\[
52x = 18
\]
\[
x = \frac{18}{52} = \frac{9}{26}
\]

Thus, we can represent the solution like this:

\[
52x - 9 = 9 \quad \text{and} \quad x \neq \text{undefined value}
\]

However, from the given options, the equation seems to be best expressed simply:

**Final Answer:**
\( 52x - 9 = 9 \quad \text{and} \quad x \neq \text{a specific value, if necessary} \)

To check the options provided:

1. **Option 1:** \( 52x - 8 = 9 \) and \( x \neq -8 \)
2. **Option 2:** \( 52x - 8 - 1 = 9 \) and \( x \neq 8 \)
3. **Option 3:** \( 52x - 8 - 1 = 9 \) and \( x \neq 4 \)
4. **Option 4:** \( 52x - 8 - 1 = 9 \) and \( x \neq -4 \)

Thus, the correct response is:

**None of the provided options accurately express both original equality and appropriate restrictions.**

To write your response clearly:

\[
52x - 9 = 9 \quad \text{and} \quad x \neq \frac{9}{26}
\]

You might want to select options that maintain the same context of the initial equation.