Solve For { A$} : : : { \frac{3}{4} A + 7 = 79 \}

Introduction

In mathematics, solving linear equations is a fundamental concept that helps us find the value of a variable. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving a linear equation with one variable, specifically the equation $\frac{3}{4} a + 7 = 79$. We will use a step-by-step approach to isolate the variable and find the value of $a$.

Understanding the Equation

Before we start solving the equation, let's understand what it means. The equation $\frac{3}{4} a + 7 = 79$ states that the product of $\frac{3}{4}$ and $a$ plus 7 is equal to 79. Our goal is to isolate the variable $a$ and find its value.

Step 1: Subtract 7 from Both Sides

To isolate the variable $a$, we need to get rid of the constant term 7. We can do this by subtracting 7 from both sides of the equation. This will give us:

$\frac{3}{4} a + 7 - 7 = 79 - 7$

Simplifying the equation, we get:

$\frac{3}{4} a = 72$

Step 2: Multiply Both Sides by the Reciprocal of $\frac{3}{4}$

To isolate the variable $a$, we need to get rid of the coefficient $\frac{3}{4}$. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{3}{4}$, which is $\frac{4}{3}$. This will give us:

$\frac{4}{3} \cdot \frac{3}{4} a = \frac{4}{3} \cdot 72$

Simplifying the equation, we get:

$a = 96$

Conclusion

In this article, we solved the linear equation $\frac{3}{4} a + 7 = 79$ using a step-by-step approach. We first subtracted 7 from both sides to isolate the term with the variable, and then multiplied both sides by the reciprocal of the coefficient to get rid of it. This gave us the value of $a$, which is 96.

Tips and Tricks

• When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you perform the operations in the correct order.
• When multiplying or dividing both sides of an equation by a fraction, make sure to multiply or divide both sides by the reciprocal of the fraction.
• When solving linear equations, it's helpful to use a step-by-step approach to ensure that you don't make any mistakes.

Real-World Applications

Solving linear equations has many real-world applications, including:

• Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
• Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
• Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Common Mistakes to Avoid

• When solving linear equations, it's easy to make mistakes by not following the order of operations or by not multiplying or dividing both sides of the equation by the correct fraction.
• When solving linear equations, it's also easy to make mistakes by not checking your work or by not using a step-by-step approach.

Final Thoughts

Solving linear equations is a fundamental concept in mathematics that has many real-world applications. By following a step-by-step approach and using the correct techniques, you can solve linear equations with ease. Remember to always follow the order of operations, multiply or divide both sides of the equation by the correct fraction, and check your work to ensure that you get the correct answer.

Introduction

In our previous article, we discussed how to solve linear equations using a step-by-step approach. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. For example, the equation $2x + 3 = 5$ is a linear equation because the highest power of the variable $x$ is 1.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

• The equation has only one variable (or multiple variables with the same power).
• The highest power of the variable(s) is 1.
• The equation does not contain any exponents or roots.

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

A: A linear equation has the highest power of the variable(s) as 1, while a quadratic equation has the highest power of the variable(s) as 2. For example, the equation $x^2 + 2x + 1 = 0$ is a quadratic equation because the highest power of the variable $x$ is 2.

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

A: To solve a linear equation with fractions, follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
2. Simplify the equation by canceling out any common factors.
3. Solve for the variable using the standard techniques for solving linear equations.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the underlying math and be able to solve the equation by hand. This will help you to:

• Check your work and ensure that the calculator is giving you the correct answer.
• Understand the concept of solving linear equations and apply it to more complex problems.
• Develop problem-solving skills and critical thinking.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not following the order of operations (PEMDAS).
• Not multiplying or dividing both sides of the equation by the correct fraction.
• Not checking your work or using a step-by-step approach.
• Not using the correct techniques for solving linear equations.

Q: Can I use algebraic manipulations to solve linear equations?

A: Yes, you can use algebraic manipulations to solve linear equations. Some common techniques include:

• Adding or subtracting the same value to both sides of the equation.
• Multiplying or dividing both sides of the equation by the same value.
• Using inverse operations to isolate the variable.

Q: How do I know if an equation is a linear equation or a quadratic equation?

A: To determine if an equation is a linear equation or a quadratic equation, look for the following characteristics:

• Linear equation: The highest power of the variable(s) is 1.
• Quadratic equation: The highest power of the variable(s) is 2.

Q: Can I use linear equations to model real-world problems?

A: Yes, you can use linear equations to model real-world problems. Some examples include:

• Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
• Science: Linear equations can be used to model population growth, chemical reactions, and other scientific phenomena.
• Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Conclusion

Solving linear equations is a fundamental concept in mathematics that has many real-world applications. By understanding the underlying math and using the correct techniques, you can solve linear equations with ease. Remember to always follow the order of operations, multiply or divide both sides of the equation by the correct fraction, and check your work to ensure that you get the correct answer.