Question

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Determine whether the equation below has a one solution, no solutions, or an infinite number of solutions. Afterwards, determine two values of x*x* that support your conclusion. 

x, minus, 5, equals, 4

*x*−5=

4

Answer

Attempt 1 out of 2

The equation has Select an optionone solutioninfinite solutionsno solutions.

Let's solve the equation step by step:

Given equation:

\[ x - 5 = 4 \]

To solve for \( x \), add 5 to both sides of the equation:

\[
x - 5 + 5 = 4 + 5
\]

This simplifies to:

\[
x = 9
\]

### Conclusion:
The equation has **one solution** because we have found a specific value of \( x \) that satisfies the equation.

### Verification:
To verify, substitute \( x = 9 \) back into the original equation:

\[
9 - 5 = 4
\]

This is true, so the solution is correct. The value \( x = 9 \) supports the conclusion that the equation has one solution.

### Answer:
- The equation has **one solution**.
- The value of \( x \) that supports this conclusion is \( x = 9 \).

Would you like more details, or do you have any other questions?

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Here are 8 related questions to expand your understanding:

1. What is the general process for solving linear equations?
2. How can you verify the number of solutions to a linear equation?
3. What does it mean when a linear equation has infinite solutions?
4. How can you identify an equation with no solutions?
5. What are the different types of solutions for quadratic equations?
6. How do you solve equations involving variables on both sides?
7. Can linear equations have more than one solution? If so, under what conditions?
8. How do you solve equations that involve fractions?

**Tip:** Always verify your solution by substituting it back into the original equation to ensure accuracy.

Understand how to determine the number of solutions for the linear equation x - 5 = 4. This problem involves basic algebraic concepts and solution verification techniques. Suitable for students in Grades 6-8.

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