Consider The Equation X 5 − 2 = 11 \frac{x}{5} - 2 = 11 5 X ​ − 2 = 11 .Each Of These Values Might Be The Solution To This Equation. Verify The Correct Solution By Substituting Each Value Into The Equation. Which Is The Correct Solution?A. X = 1.8 X = 1.8 X = 1.8 B. $x

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Introduction

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In mathematics, solving equations is a crucial skill that helps us find the value of unknown variables. In this article, we will focus on solving a linear equation, specifically the equation $\frac{x}{5} - 2 = 11$. We will explore the process of solving this equation and verify the correct solution by substituting each value into the equation.

The Equation

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The given equation is $\frac{x}{5} - 2 = 11$. Our goal is to find the value of $x$ that satisfies this equation.

Step 1: Add 2 to Both Sides

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To isolate the term involving $x$, we need to get rid of the constant term on the left-hand side. We can do this by adding 2 to both sides of the equation.

$\frac{x}{5} - 2 + 2 = 11 + 2$

This simplifies to:

$\frac{x}{5} = 13$

Step 2: Multiply Both Sides by 5

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To get rid of the fraction, we can multiply both sides of the equation by 5.

$\frac{x}{5} \times 5 = 13 \times 5$

This simplifies to:

$x = 65$

Verifying the Solution

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Now that we have found the value of $x$, we need to verify that it is indeed the correct solution. We can do this by substituting $x = 65$ into the original equation.

$\frac{65}{5} - 2 = 11$

This simplifies to:

$13 - 2 = 11$

Which is true.

Conclusion

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In this article, we solved the equation $\frac{x}{5} - 2 = 11$ by adding 2 to both sides and then multiplying both sides by 5. We found that the value of $x$ that satisfies this equation is $x = 65$. We verified this solution by substituting $x = 65$ into the original equation.

Alternative Solutions

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Let's consider the alternative solutions given in the problem statement: $x = 1.8$ and $x = 70$. We can verify these solutions by substituting them into the original equation.

Solution A: $x = 1.8$

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$\frac{1.8}{5} - 2 = 11$

This simplifies to:

$0.36 - 2 = 11$

Which is not true.

Solution B: $x = 70$

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$\frac{70}{5} - 2 = 11$

This simplifies to:

$14 - 2 = 11$

Which is not true.

Conclusion

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In conclusion, the correct solution to the equation $\frac{x}{5} - 2 = 11$ is $x = 65$. We verified this solution by substituting it into the original equation. The alternative solutions given in the problem statement, $x = 1.8$ and $x = 70$, are not correct.

Final Answer

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The final answer is: $\boxed{65}$

=====================================================

Introduction

---

In mathematics, solving equations is a crucial skill that helps us find the value of unknown variables. In this article, we will focus on solving a linear equation, specifically the equation $\frac{x}{5} - 2 = 11$. We will explore the process of solving this equation and verify the correct solution by substituting each value into the equation.

The Equation

---

The given equation is $\frac{x}{5} - 2 = 11$. Our goal is to find the value of $x$ that satisfies this equation.

Step 1: Add 2 to Both Sides

---

To isolate the term involving $x$, we need to get rid of the constant term on the left-hand side. We can do this by adding 2 to both sides of the equation.

$\frac{x}{5} - 2 + 2 = 11 + 2$

This simplifies to:

$\frac{x}{5} = 13$

Step 2: Multiply Both Sides by 5

---

To get rid of the fraction, we can multiply both sides of the equation by 5.

$\frac{x}{5} \times 5 = 13 \times 5$

This simplifies to:

$x = 65$

Verifying the Solution

---

Now that we have found the value of $x$, we need to verify that it is indeed the correct solution. We can do this by substituting $x = 65$ into the original equation.

$\frac{65}{5} - 2 = 11$

This simplifies to:

$13 - 2 = 11$

Which is true.

Conclusion

---

In this article, we solved the equation $\frac{x}{5} - 2 = 11$ by adding 2 to both sides and then multiplying both sides by 5. We found that the value of $x$ that satisfies this equation is $x = 65$. We verified this solution by substituting $x = 65$ into the original equation.

Alternative Solutions

---

Let's consider the alternative solutions given in the problem statement: $x = 1.8$ and $x = 70$. We can verify these solutions by substituting them into the original equation.

Solution A: $x = 1.8$

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$\frac{1.8}{5} - 2 = 11$

This simplifies to:

$0.36 - 2 = 11$

Which is not true.

Solution B: $x = 70$

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$\frac{70}{5} - 2 = 11$

This simplifies to:

$14 - 2 = 11$

Which is not true.

Conclusion

---

In conclusion, the correct solution to the equation $\frac{x}{5} - 2 = 11$ is $x = 65$. We verified this solution by substituting it into the original equation. The alternative solutions given in the problem statement, $x = 1.8$ and $x = 70$, are not correct.

Final Answer

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The final answer is: $\boxed{65}$

Q&A

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Q: What is the equation we are solving?

A: The equation we are solving is $\frac{x}{5} - 2 = 11$.

Q: How do we isolate the term involving $x$?

A: We can isolate the term involving $x$ by adding 2 to both sides of the equation.

Q: What is the value of $x$ that satisfies the equation?

A: The value of $x$ that satisfies the equation is $x = 65$.

Q: How do we verify the solution?

A: We can verify the solution by substituting the value of $x$ into the original equation.

Q: What are the alternative solutions given in the problem statement?

A: The alternative solutions given in the problem statement are $x = 1.8$ and $x = 70$.

Q: Are the alternative solutions correct?

A: No, the alternative solutions are not correct.

Q: What is the final answer?

A: The final answer is $\boxed{65}$.

Common Mistakes

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Mistake 1: Not isolating the term involving $x$

A: Make sure to isolate the term involving $x$ by adding or subtracting the same value from both sides of the equation.

Mistake 2: Not verifying the solution

A: Make sure to verify the solution by substituting the value of $x$ into the original equation.

Mistake 3: Not considering alternative solutions

A: Make sure to consider alternative solutions and verify them by substituting the values into the original equation.

Conclusion

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In conclusion, solving the equation $\frac{x}{5} - 2 = 11$ requires careful steps and verification of the solution. By following the steps outlined in this article, you can find the correct solution and avoid common mistakes.