Consider The Numbers $2, 6, 7$, And $12$. Which Of These Numbers, If Any, Is A Solution To $\frac{1}{2}(3x+4)=11$?Show How You Know.

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Introduction

In this article, we will explore the given equation $\frac{1}{2}(3x+4)=11$ and determine which of the numbers $2, 6, 7$, and $12$ is a solution to this equation. We will use algebraic techniques to solve for $x$ and then check each of the given numbers to see if it satisfies the equation.

Step 1: Multiply Both Sides by 2

To begin solving the equation, we can start by multiplying both sides of the equation by 2 to eliminate the fraction. This gives us:

$$3x+4=22$$

Step 2: Subtract 4 from Both Sides

Next, we can subtract 4 from both sides of the equation to isolate the term with $x$. This gives us:

$$3x=18$$

Step 3: Divide Both Sides by 3

Finally, we can divide both sides of the equation by 3 to solve for $x$. This gives us:

$$x=6$$

Checking the Solutions

Now that we have found the value of $x$, we can check each of the given numbers to see if it satisfies the equation. We will substitute each number into the original equation and see if it is true.

Checking $x=2$

Substituting $x=2$ into the original equation, we get:

$$\frac{1}{2}(3(2)+4)=\frac{1}{2}(6+4)=\frac{1}{2}(10)=5$$

This is not equal to 11, so $x=2$ is not a solution.

Checking $x=6$

Substituting $x=6$ into the original equation, we get:

$$\frac{1}{2}(3(6)+4)=\frac{1}{2}(18+4)=\frac{1}{2}(22)=11$$

This is equal to 11, so $x=6$ is a solution.

Checking $x=7$

Substituting $x=7$ into the original equation, we get:

$$\frac{1}{2}(3(7)+4)=\frac{1}{2}(21+4)=\frac{1}{2}(25)=12.5$$

This is not equal to 11, so $x=7$ is not a solution.

Checking $x=12$

Substituting $x=12$ into the original equation, we get:

$$\frac{1}{2}(3(12)+4)=\frac{1}{2}(36+4)=\frac{1}{2}(40)=20$$

This is not equal to 11, so $x=12$ is not a solution.

Conclusion

In this article, we solved the equation $\frac{1}{2}(3x+4)=11$ and found that $x=6$ is a solution. We also checked the other given numbers and found that they are not solutions. This demonstrates the importance of checking solutions in algebra and the need to be careful when substituting values into equations.

Final Answer

The final answer is $\boxed{6}$.

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Introduction

In our previous article, we solved the equation $\frac{1}{2}(3x+4)=11$ and found that $x=6$ is a solution. In this article, we will answer some frequently asked questions (FAQs) about solving this equation.

Q: What is the first step in solving the equation $\frac{1}{2}(3x+4)=11$?

A: The first step in solving the equation $\frac{1}{2}(3x+4)=11$ is to multiply both sides of the equation by 2 to eliminate the fraction. This gives us $3x+4=22$.

Q: Why do we need to multiply both sides of the equation by 2?

A: We need to multiply both sides of the equation by 2 to eliminate the fraction. This makes it easier to solve for $x$.

Q: What is the next step in solving the equation $\frac{1}{2}(3x+4)=11$?

A: The next step in solving the equation $\frac{1}{2}(3x+4)=11$ is to subtract 4 from both sides of the equation to isolate the term with $x$. This gives us $3x=18$.

Q: Why do we need to subtract 4 from both sides of the equation?

A: We need to subtract 4 from both sides of the equation to isolate the term with $x$. This makes it easier to solve for $x$.

Q: What is the final step in solving the equation $\frac{1}{2}(3x+4)=11$?

A: The final step in solving the equation $\frac{1}{2}(3x+4)=11$ is to divide both sides of the equation by 3 to solve for $x$. This gives us $x=6$.

Q: Why do we need to divide both sides of the equation by 3?

A: We need to divide both sides of the equation by 3 to solve for $x$. This gives us the value of $x$ that satisfies the equation.

Q: How do we check if a number is a solution to the equation $\frac{1}{2}(3x+4)=11$?

A: To check if a number is a solution to the equation $\frac{1}{2}(3x+4)=11$, we substitute the number into the original equation and see if it is true.

Q: What is the importance of checking solutions in algebra?

A: The importance of checking solutions in algebra is to ensure that the solution we found is correct. If we don't check our solutions, we may end up with an incorrect answer.

Q: What is the final answer to the equation $\frac{1}{2}(3x+4)=11$?

A: The final answer to the equation $\frac{1}{2}(3x+4)=11$ is $x=6$.

Conclusion

In this article, we answered some frequently asked questions (FAQs) about solving the equation $\frac{1}{2}(3x+4)=11$. We covered topics such as the first step in solving the equation, why we need to multiply both sides of the equation by 2, and how to check if a number is a solution to the equation. We hope this article has been helpful in understanding how to solve the equation $\frac{1}{2}(3x+4)=11$.

Final Answer

The final answer is $\boxed{6}$.