Determine whether the equation below has a one solution, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion.
start fraction, 46, divided by, x, end fraction, equals, 2
x
46
​
 =
2

The equation you provided is:

\[
\frac{46}{x} = 2
\]

To determine whether it has one solution, no solutions, or an infinite number of solutions, we need to solve for \( x \).

### Step 1: Solve for \( x \)

Multiply both sides of the equation by \( x \) to eliminate the fraction:

\[
46 = 2x
\]

### Step 2: Isolate \( x \)

Divide both sides of the equation by 2:

\[
x = \frac{46}{2} = 23
\]

### Conclusion:
The equation has **one solution**, \( x = 23 \).

### Step 3: Verify with another value for \( x \)
To verify, substitute \( x = 23 \) back into the original equation:

\[
\frac{46}{23} = 2
\]

This holds true, confirming that \( x = 23 \) is a valid solution. 

For this specific equation, there is **only one solution**, and the only value of \( x \) that satisfies the equation is \( x = 23 \). There are **no other values** that satisfy the equation.

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Would you like more details, or do you have any questions about this process?

Here are 5 related questions:
1. How do you solve equations involving variables in both the numerator and denominator?
2. What happens if the variable appears in the denominator with more complex expressions?
3. How can we check if an equation has no solutions or infinite solutions?
4. What are some common errors when solving rational equations?
5. Can equations of this type have negative solutions?

**Tip:** Always check your solutions by substituting them back into the original equation to verify that they satisfy the equation.

Determine whether the equation below has one solution, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion: 46/x = 2.

Learn how to solve the rational equation 46/x = 2 with step-by-step guidance. This solution covers key algebraic concepts, including isolating variables and verifying solutions. Suitable for students in Grades 6-8.

Math Problem Statement

Determine whether the equation below has a one solution, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion. start fraction, 46, divided by, x, end fraction, equals, 2 x 46

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