If $\frac{x}{3}+\frac{x}{4}+15=x$, Then $x =$A. 18 B. 24 C. 36 D. 48 E. 60

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear equation, which involves fractions and constants. We will use the given equation $\frac{x}{3}+\frac{x}{4}+15=x$ to demonstrate the step-by-step process of solving linear equations.

Understanding the Equation

The given equation is $\frac{x}{3}+\frac{x}{4}+15=x$. To solve this equation, we need to isolate the variable $x$ on one side of the equation. The equation involves fractions, which can be challenging to work with. However, with the correct approach, we can simplify the equation and solve for $x$.

Step 1: Simplify the Fractions

The first step is to simplify the fractions in the equation. We can do this by finding the least common multiple (LCM) of the denominators, which are 3 and 4. The LCM of 3 and 4 is 12. We can rewrite the fractions with a denominator of 12:

$$\frac{x}{3}=\frac{4x}{12}$$

$$\frac{x}{4}=\frac{3x}{12}$$

Now, we can rewrite the equation as:

$$\frac{4x}{12}+\frac{3x}{12}+15=x$$

Step 2: Combine Like Terms

The next step is to combine the like terms in the equation. We can do this by adding the fractions:

$$\frac{4x+3x}{12}+15=x$$

$$\frac{7x}{12}+15=x$$

Step 3: Subtract 15 from Both Sides

To isolate the variable $x$, we need to subtract 15 from both sides of the equation:

$$\frac{7x}{12}=x-15$$

Step 4: Multiply Both Sides by 12

To eliminate the fraction, we can multiply both sides of the equation by 12:

$$7x=12(x-15)$$

Step 5: Distribute the 12

We can distribute the 12 to the terms inside the parentheses:

$$7x=12x-180$$

Step 6: Subtract 12x from Both Sides

To isolate the variable $x$, we need to subtract 12x from both sides of the equation:

$$-5x=-180$$

Step 7: Divide Both Sides by -5

Finally, we can divide both sides of the equation by -5 to solve for $x$:

$$x=36$$

Conclusion

In this article, we demonstrated the step-by-step process of solving a linear equation involving fractions and constants. We used the given equation $\frac{x}{3}+\frac{x}{4}+15=x$ to illustrate the process. By simplifying the fractions, combining like terms, subtracting 15 from both sides, multiplying both sides by 12, distributing the 12, subtracting 12x from both sides, and dividing both sides by -5, we were able to solve for $x$ and find the value of $x$ to be 36.

Answer

The correct answer is C. 36.

Additional Tips and Resources

• To solve linear equations involving fractions, it's essential to simplify the fractions first.
• Combining like terms can help simplify the equation and make it easier to solve.
• When subtracting or adding fractions, make sure to have the same denominator.
• Multiplying both sides of the equation by a constant can help eliminate fractions.
• Distributing the constant to the terms inside the parentheses can help simplify the equation.
• Finally, dividing both sides of the equation by a constant can help solve for the variable.

For more information on solving linear equations, check out the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• IXL: Solving Linear Equations

Introduction

In our previous article, we demonstrated the step-by-step process of solving a linear equation involving fractions and constants. We used the given equation $\frac{x}{3}+\frac{x}{4}+15=x$ to illustrate the process. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax+b=c$, where $a$, $b$, and $c$ are constants.

Q: How do I simplify fractions in a linear equation?

To simplify fractions in a linear equation, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. Once you have found the LCM, you can rewrite the fractions with the LCM as the denominator.

Q: What is the difference between adding and subtracting fractions?

When adding fractions, you need to have the same denominator. When subtracting fractions, you also need to have the same denominator. If the denominators are different, you need to find the LCM and rewrite the fractions with the LCM as the denominator.

Q: How do I combine like terms in a linear equation?

To combine like terms in a linear equation, you need to add or subtract the coefficients of the like terms. For example, if you have the equation $2x+3x=5x$, you can combine the like terms by adding the coefficients: $2x+3x=5x$.

Q: What is the distributive property?

The distributive property is a rule that allows you to multiply a single term to multiple terms. For example, if you have the equation $2(x+3)$, you can use the distributive property to multiply the 2 to both terms inside the parentheses: $2x+6$.

Q: How do I solve a linear equation with a fraction?

To solve a linear equation with a fraction, you need to isolate the variable. You can do this by multiplying both sides of the equation by the denominator of the fraction. This will eliminate the fraction and allow you to solve for the variable.

Q: What is the difference between a linear equation and a quadratic equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. A quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation $x+2=5$ is a linear equation, while the equation $x^2+4x+4=0$ is a quadratic equation.

Q: How do I check my solution to a linear equation?

To check your solution to a linear equation, you need to plug the solution back into the original equation and see if it is true. If the solution satisfies the equation, then it is the correct solution.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations. We covered topics such as simplifying fractions, combining like terms, and using the distributive property. We also discussed the difference between linear and quadratic equations and how to check your solution to a linear equation.

Additional Tips and Resources

• To solve linear equations, it's essential to simplify the fractions first.
• Combining like terms can help simplify the equation and make it easier to solve.
• When subtracting or adding fractions, make sure to have the same denominator.
• Multiplying both sides of the equation by a constant can help eliminate fractions.
• Distributing the constant to the terms inside the parentheses can help simplify the equation.
• Finally, dividing both sides of the equation by a constant can help solve for the variable.

For more information on solving linear equations, check out the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• IXL: Solving Linear Equations

By following these tips and practicing with different types of linear equations, you can become proficient in solving linear equations and tackle more complex math problems with confidence.