Which Value Of $x$ Makes $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ True?1) 8 2) 6 3) 0 4) 4

Introduction

In this article, we will delve into the world of algebra and solve a linear equation involving fractions. The equation in question is $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$. Our goal is to find the value of $x$ that makes this equation true. We will use various algebraic techniques to simplify the equation and isolate the variable $x$.

Understanding the Equation

The given equation is a linear equation involving fractions. It can be written as:

$$\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$$

To solve this equation, we need to get rid of the fractions. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 12.

Multiplying Both Sides by 12

Multiplying both sides of the equation by 12 gives us:

$$12\left(\frac{x-3}{4}+\frac{2}{3}\right)=12\left(\frac{17}{12}\right)$$

Using the distributive property, we can rewrite the left-hand side of the equation as:

$$3(x-3)+8=17$$

Simplifying the Equation

Now, we can simplify the equation by combining like terms:

$$3x-9+8=17$$

This simplifies to:

$$3x-1=17$$

Isolating the Variable $x$

To isolate the variable $x$, we need to get rid of the constant term on the left-hand side of the equation. We can do this by adding 1 to both sides of the equation:

$$3x=17+1$$

This simplifies to:

$$3x=18$$

Solving for $x$

Finally, we can solve for $x$ by dividing both sides of the equation by 3:

$$x=\frac{18}{3}$$

This simplifies to:

$$x=6$$

Conclusion

In this article, we solved the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ to find the value of $x$ that makes it true. We used various algebraic techniques, including multiplying both sides of the equation by the LCM of the denominators, simplifying the equation, and isolating the variable $x$. The final answer is $x=6$.

Discussion

The equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ is a linear equation involving fractions. To solve it, we need to get rid of the fractions by multiplying both sides of the equation by the LCM of the denominators. This gives us a simplified equation that we can solve using basic algebraic techniques.

Step-by-Step Solution

Here is a step-by-step solution to the equation:

1. Multiply both sides of the equation by 12 to get rid of the fractions.
2. Simplify the equation by combining like terms.
3. Isolate the variable $x$ by adding 1 to both sides of the equation.
4. Solve for $x$ by dividing both sides of the equation by 3.

Common Mistakes

When solving the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$, there are several common mistakes to avoid:

• Not multiplying both sides of the equation by the LCM of the denominators.
• Not simplifying the equation by combining like terms.
• Not isolating the variable $x$ by adding 1 to both sides of the equation.
• Not solving for $x$ by dividing both sides of the equation by 3.

Final Answer

The final answer to the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ is $x=6$.

Related Equations

Here are some related equations that you may find useful:

• $$\frac{x+2}{3}+\frac{1}{4}=\frac{5}{12}$$

• $$\frac{x-1}{2}+\frac{3}{4}=\frac{7}{8}$$

• $$\frac{x+1}{3}+\frac{2}{5}=\frac{11}{15}$$

Conclusion

In this article, we solved the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ to find the value of $x$ that makes it true. We used various algebraic techniques, including multiplying both sides of the equation by the LCM of the denominators, simplifying the equation, and isolating the variable $x$. The final answer is $x=6$.

Introduction

In our previous article, we solved the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ to find the value of $x$ that makes it true. In this article, we will answer some frequently asked questions (FAQs) related to the solution of this equation.

Q: What is the least common multiple (LCM) of the denominators in the equation?

A: The LCM of the denominators 4 and 3 is 12.

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

A: We need to multiply both sides of the equation by the LCM of the denominators to get rid of the fractions. This makes it easier to simplify the equation and isolate the variable $x$.

Q: How do we simplify the equation after multiplying both sides by the LCM of the denominators?

A: After multiplying both sides of the equation by the LCM of the denominators, we can simplify the equation by combining like terms. This involves adding or subtracting the same value to both sides of the equation.

Q: How do we isolate the variable $x$ in the equation?

A: To isolate the variable $x$, we need to get rid of the constant term on the left-hand side of the equation. We can do this by adding or subtracting the same value to both sides of the equation.

Q: What is the final answer to the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$?

A: The final answer to the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ is $x=6$.

Q: What are some common mistakes to avoid when solving the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$?

A: Some common mistakes to avoid when solving the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ include:

• Not multiplying both sides of the equation by the LCM of the denominators.
• Not simplifying the equation by combining like terms.
• Not isolating the variable $x$ by adding or subtracting the same value to both sides of the equation.
• Not solving for $x$ by dividing both sides of the equation by the coefficient of $x$.

Q: What are some related equations that I can try to solve?

A: Here are some related equations that you can try to solve:

• $$\frac{x+2}{3}+\frac{1}{4}=\frac{5}{12}$$

• $$\frac{x-1}{2}+\frac{3}{4}=\frac{7}{8}$$

• $$\frac{x+1}{3}+\frac{2}{5}=\frac{11}{15}$$

Q: How can I practice solving equations like $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$?

A: You can practice solving equations like $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$ by trying to solve similar equations on your own. You can also use online resources or math textbooks to find more practice problems.

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to the solution of the equation $\frac{x-3}{4}+\frac{2}{3}=\frac{17}{12}$. We covered topics such as the least common multiple (LCM) of the denominators, simplifying the equation, isolating the variable $x$, and common mistakes to avoid. We also provided some related equations and tips for practicing solving equations like this one.