Solve The Equation For $C$:$M=\frac{4}{5} C-12$$ C = C= C = [/tex]

Introduction

In mathematics, equations are a fundamental concept that helps us solve problems and understand relationships between variables. In this article, we will focus on solving a linear equation for the variable C. The equation is given as:

$$M = \frac{4}{5}C - 12$$

Our goal is to isolate the variable C and find its value. We will use algebraic techniques to solve this equation and provide a step-by-step guide on how to do it.

Understanding the Equation

Before we start solving the equation, let's understand what it means. The equation is a linear equation, which means it is in the form of:

$$ax + b = c$$

where a, b, and c are constants, and x is the variable. In our equation, M is the variable, and C is the constant that we want to solve for.

Step 1: Add 12 to Both Sides

To isolate the variable C, we need to get rid of the constant term -12. We can do this by adding 12 to both sides of the equation. This will give us:

$$M + 12 = \frac{4}{5}C - 12 + 12$$

Simplifying the right-hand side, we get:

$$M + 12 = \frac{4}{5}C$$

Step 2: Multiply Both Sides by 5

To get rid of the fraction, we can multiply both sides of the equation by 5. This will give us:

$$5(M + 12) = 5 \times \frac{4}{5}C$$

Simplifying the right-hand side, we get:

$$5M + 60 = 4C$$

Step 3: Divide Both Sides by 4

Now, we can divide both sides of the equation by 4 to isolate the variable C. This will give us:

$$\frac{5M + 60}{4} = C$$

Solving for C

Now that we have isolated the variable C, we can solve for its value. We can do this by plugging in the value of M into the equation. Let's say M = 20. Plugging this value into the equation, we get:

$$\frac{5(20) + 60}{4} = C$$

Simplifying the left-hand side, we get:

$$\frac{100 + 60}{4} = C$$

$$\frac{160}{4} = C$$

$$40 = C$$

Conclusion

In this article, we solved the equation for C using algebraic techniques. We started by adding 12 to both sides of the equation, then multiplied both sides by 5, and finally divided both sides by 4 to isolate the variable C. We found that the value of C is 40. This demonstrates the importance of algebra in solving equations and understanding relationships between variables.

Tips and Tricks

• When solving equations, always start by isolating the variable you want to solve for.
• Use algebraic techniques such as adding, subtracting, multiplying, and dividing to simplify the equation.
• Be careful when multiplying or dividing both sides of the equation by a fraction.
• Always check your work by plugging in the value of the variable into the original equation.

Real-World Applications

Solving equations is a fundamental concept in mathematics that has many real-world applications. Some examples include:

• Physics: Solving equations is used to describe the motion of objects and understand the relationships between variables such as velocity, acceleration, and time.
• Engineering: Solving equations is used to design and optimize systems such as bridges, buildings, and electronic circuits.
• Economics: Solving equations is used to understand the relationships between variables such as supply and demand, and to make predictions about economic trends.

Final Thoughts

Introduction

In our previous article, we solved the equation for C using algebraic techniques. We started by adding 12 to both sides of the equation, then multiplied both sides by 5, and finally divided both sides by 4 to isolate the variable C. We found that the value of C is 40. In this article, we will answer some frequently asked questions about solving equations and provide additional tips and tricks to help you become proficient in solving equations.

Q&A

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

A: The first step in solving an equation is to isolate the variable you want to solve for. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by a constant.

Q: How do I know which operation to use to isolate the variable?

A: To determine which operation to use, look at the coefficient of the variable. If the coefficient is a fraction, multiply both sides of the equation by the denominator of the fraction. If the coefficient is a whole number, add or subtract the opposite of the coefficient to both sides of the equation.

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

A: A linear equation is an equation in which the highest power of the variable is 1. A quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation 2x + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Q: What is the importance of checking your work?

A: Checking your work is essential when solving equations. It ensures that your solution is correct and that you have not made any mistakes. To check your work, plug the value of the variable into the original equation and verify that it is true.

Q: How do I know if an equation has a solution?

A: To determine if an equation has a solution, try to isolate the variable. If you can isolate the variable, then the equation has a solution. If you cannot isolate the variable, then the equation may not have a solution.

Q: What is the difference between a system of equations and a single equation?

A: A system of equations is a set of two or more equations that are solved simultaneously. A single equation is a single equation that is solved independently. For example, the equations 2x + 3 = 5 and x - 2 = 3 are a system of equations, while the equation 2x + 3 = 5 is a single equation.

Q: How do I solve a system of equations?

A: To solve a system of equations, use the method of substitution or elimination. The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation. The method of elimination involves adding or subtracting the equations to eliminate one variable.

Tips and Tricks

• Always start by isolating the variable you want to solve for.
• Use algebraic techniques such as adding, subtracting, multiplying, and dividing to simplify the equation.
• Be careful when multiplying or dividing both sides of the equation by a fraction.
• Always check your work by plugging in the value of the variable into the original equation.
• Use the quadratic formula to solve quadratic equations.
• Use the method of substitution or elimination to solve systems of equations.

Real-World Applications

Solving equations is a fundamental concept in mathematics that has many real-world applications. Some examples include:

• Physics: Solving equations is used to describe the motion of objects and understand the relationships between variables such as velocity, acceleration, and time.
• Engineering: Solving equations is used to design and optimize systems such as bridges, buildings, and electronic circuits.
• Economics: Solving equations is used to understand the relationships between variables such as supply and demand, and to make predictions about economic trends.

Final Thoughts

Solving equations is a crucial skill in mathematics that has many real-world applications. By following the steps outlined in this article and practicing regularly, you can become proficient in solving equations and apply this skill to real-world problems. Remember to always start by isolating the variable you want to solve for, and use algebraic techniques such as adding, subtracting, multiplying, and dividing to simplify the equation. With practice and patience, you can become proficient in solving equations and apply this skill to real-world problems.