Solve The Equation:$\frac{1}{4}(d-3)=-15$

$$

Introduction

In mathematics, equations are a fundamental concept that helps us solve problems and understand various mathematical concepts. One of the most common types of equations is linear equations, which can be solved using various methods such as algebraic manipulation, graphing, and substitution. In this article, we will focus on solving a linear equation involving fractions, specifically the equation $\frac{1}{4}(d-3)=-15$. We will use algebraic manipulation to solve for the variable $d$.

Understanding the Equation

The given equation is $\frac{1}{4}(d-3)=-15$. This equation involves a fraction, which can be challenging to solve. However, with the correct approach, we can simplify the equation and solve for the variable $d$. The first step is to understand the equation and identify the operations involved. In this equation, we have a fraction $\frac{1}{4}$ multiplied by the expression $(d-3)$, which is equal to $-15$.

Distributing the Fraction

To solve the equation, we need to distribute the fraction $\frac{1}{4}$ to the expression $(d-3)$. This can be done by multiplying the fraction by each term inside the parentheses. Using the distributive property, we can write:

$$\frac{1}{4}(d-3) = \frac{1}{4}d - \frac{1}{4} \cdot 3$$

Simplifying the expression, we get:

$$\frac{1}{4}d - \frac{3}{4} = -15$$

Isolating the Variable

Now that we have simplified the equation, we can isolate the variable $d$ by adding $\frac{3}{4}$ to both sides of the equation. This will help us eliminate the fraction and make it easier to solve for $d$. Adding $\frac{3}{4}$ to both sides, we get:

$$\frac{1}{4}d = -15 + \frac{3}{4}$$

To add $-15$ and $\frac{3}{4}$, we need to find a common denominator, which is $4$. We can rewrite $-15$ as $-60$ with a denominator of $4$. Now we can add the two fractions:

$$\frac{1}{4}d = -60 + \frac{3}{4}$$

Simplifying the expression, we get:

$$\frac{1}{4}d = -\frac{57}{4}$$

Solving for the Variable

Now that we have isolated the variable $d$, we can solve for it by multiplying both sides of the equation by $4$. This will help us eliminate the fraction and find the value of $d$. Multiplying both sides by $4$, we get:

$$d = -\frac{57}{4} \cdot 4$$

Simplifying the expression, we get:

$$d = -57$$

Conclusion

In this article, we solved the equation $\frac{1}{4}(d-3)=-15$ using algebraic manipulation. We distributed the fraction, isolated the variable, and solved for $d$. The final solution is $d = -57$. This equation is a great example of how to solve linear equations involving fractions. By following the correct steps and using algebraic manipulation, we can solve even the most challenging equations.

Tips and Tricks

• When solving equations involving fractions, it's essential to distribute the fraction to the expression inside the parentheses.
• To isolate the variable, add or subtract the same value to both sides of the equation.
• When multiplying both sides of the equation by a value, make sure to multiply both sides by the same value.
• Practice solving equations involving fractions to become more comfortable with the process.

Frequently Asked Questions

• Q: What is the value of $d$ in the equation $\frac{1}{4}(d-3)=-15$? A: The value of $d$ is $-57$.
• Q: How do I solve equations involving fractions? A: To solve equations involving fractions, distribute the fraction to the expression inside the parentheses, isolate the variable, and solve for the variable.
• Q: What is the importance of algebraic manipulation in solving equations? A: Algebraic manipulation is essential in solving equations, as it helps us simplify the equation and isolate the variable.

Final Thoughts

Solving equations involving fractions can be challenging, but with the correct approach and practice, it becomes easier. In this article, we solved the equation $\frac{1}{4}(d-3)=-15$ using algebraic manipulation. We distributed the fraction, isolated the variable, and solved for $d$. The final solution is $d = -57$. By following the correct steps and using algebraic manipulation, we can solve even the most challenging equations.

Introduction

Solving equations involving fractions can be a challenging task, but with the right approach and practice, it becomes easier. In our previous article, we solved the equation $\frac{1}{4}(d-3)=-15$ using algebraic manipulation. In this article, we will answer some frequently asked questions about solving equations involving fractions.

Q&A

Q: What is the first step in solving an equation involving fractions?

A: The first step in solving an equation involving fractions is to distribute the fraction to the expression inside the parentheses. This can be done by multiplying the fraction by each term inside the parentheses.

Q: How do I simplify an equation involving fractions?

A: To simplify an equation involving fractions, you can use the distributive property to distribute the fraction to the expression inside the parentheses. You can also add or subtract the same value to both sides of the equation to eliminate the fraction.

Q: What is the importance of isolating the variable in an equation involving fractions?

A: Isolating the variable in an equation involving fractions is essential to solve for the variable. By isolating the variable, you can eliminate the fraction and find the value of the variable.

Q: How do I multiply both sides of an equation by a value?

A: To multiply both sides of an equation by a value, you need to multiply both sides by the same value. This will help you eliminate the fraction and find the value of the variable.

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

A: Adding and subtracting fractions involves finding a common denominator and adding or subtracting the numerators. When adding fractions, you add the numerators and keep the denominator the same. When subtracting fractions, you subtract the numerators and keep the denominator the same.

Q: How do I solve an equation involving fractions with a negative sign?

A: To solve an equation involving fractions with a negative sign, you need to follow the same steps as solving an equation involving fractions without a negative sign. However, you need to be careful when multiplying both sides of the equation by a negative value.

Q: What is the final step in solving an equation involving fractions?

A: The final step in solving an equation involving fractions is to check your solution by plugging it back into the original equation. This will help you ensure that your solution is correct.

Tips and Tricks

• When solving equations involving fractions, it's essential to distribute the fraction to the expression inside the parentheses.
• To simplify an equation involving fractions, use the distributive property and add or subtract the same value to both sides of the equation.
• Isolating the variable is essential to solve for the variable.
• When multiplying both sides of an equation by a value, make sure to multiply both sides by the same value.
• Practice solving equations involving fractions to become more comfortable with the process.

Real-World Applications

Solving equations involving fractions has many real-world applications. For example:

• In finance, you may need to solve equations involving fractions to calculate interest rates or investment returns.
• In science, you may need to solve equations involving fractions to calculate the concentration of a solution or the rate of a chemical reaction.
• In engineering, you may need to solve equations involving fractions to calculate the stress or strain on a material.

Conclusion

Solving equations involving fractions can be a challenging task, but with the right approach and practice, it becomes easier. In this article, we answered some frequently asked questions about solving equations involving fractions. We also provided some tips and tricks to help you become more comfortable with the process. By following the correct steps and using algebraic manipulation, you can solve even the most challenging equations.

Final Thoughts

Solving equations involving fractions is an essential skill that has many real-world applications. By practicing and becoming more comfortable with the process, you can solve even the most challenging equations and apply your skills to real-world problems.