C Times (-12) + 15= (-9)

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific type of linear equation, c times (-12) + 15 = (-9). We will break down the solution step by step, using simple language and examples to make it easy to understand.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, c) is 1. It is called "linear" because it can be graphed as a straight line on a coordinate plane. Linear equations can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.

The Equation c times (-12) + 15 = (-9)

The equation c times (-12) + 15 = (-9) is a linear equation that involves a variable (c) and constants. To solve for c, we need to isolate the variable on one side of the equation.

Step 1: Simplify the Equation

The first step in solving the equation is to simplify it by evaluating the expression c times (-12). This means multiplying c by -12.

c * (-12) = -12c

So, the equation becomes:

-12c + 15 = -9

Step 2: Isolate the Variable

To isolate the variable c, we need to get rid of the constant term (+15) on the left side of the equation. We can do this by subtracting 15 from both sides of the equation.

-12c + 15 - 15 = -9 - 15

This simplifies to:

-12c = -24

Step 3: Solve for c

Now that we have isolated the variable c, we can solve for its value. To do this, we need to get rid of the coefficient (-12) that is being multiplied by c. We can do this by dividing both sides of the equation by -12.

(-12c) / (-12) = (-24) / (-12)

This simplifies to:

c = 2

Conclusion

In this article, we solved the linear equation c times (-12) + 15 = (-9) step by step. We simplified the equation, isolated the variable, and solved for its value. The final answer is c = 2.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • To isolate the variable, you can add, subtract, multiply, or divide both sides of the equation by the same value.
  • When solving for a variable, make sure to check your work by plugging the solution back into the original equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Common Mistakes

  • Not following the order of operations (PEMDAS)
  • Not isolating the variable correctly
  • Not checking the solution by plugging it back into the original equation

Final Thoughts

Solving linear equations is a crucial skill that has numerous real-world applications. By following the steps outlined in this article, you can solve linear equations with ease. Remember to simplify the equation, isolate the variable, and solve for its value. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.

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Introduction

Solving linear equations can be a challenging task, especially for those who are new to mathematics. In this article, we will address some of the most frequently asked questions about solving linear equations, including tips, tricks, and common mistakes to avoid.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, c) is 1. It is called "linear" because it can be graphed as a straight line on a coordinate plane.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to evaluate any expressions that involve variables or constants. For example, if you have the equation c times (-12) + 15 = (-9), you would simplify it by multiplying c by -12.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable, you need to get rid of any constants or coefficients that are being multiplied by the variable. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

  • P: Parentheses (evaluate expressions inside parentheses first)
  • E: Exponents (evaluate any exponential expressions next)
  • M: Multiplication and Division (perform multiplication and division operations from left to right)
  • A: Addition and Subtraction (perform addition and subtraction operations from left to right)

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 isolating the variable correctly
  • Not checking the solution by plugging it back into the original equation
  • Not simplifying the equation before solving for the variable

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

A: 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 is correct, the equation should be true. If the solution is incorrect, the equation will not be true.

Q: What are some real-world applications of linear equations?

A: Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Q: Can you provide some examples of linear equations?

A: Yes, here are some examples of linear equations:

  • 2x + 3 = 7
  • x - 4 = 2
  • 3x + 2 = 11
  • x + 2 = 9

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

A: To solve a linear equation with fractions, you need to follow the same steps as solving a linear equation with whole numbers. However, you may need to multiply both sides of the equation by a common denominator to eliminate the fractions.

Q: Can you provide some tips for solving linear equations?

A: Yes, here are some tips for solving linear equations:

  • Read the equation carefully and identify the variable and the constants.
  • Simplify the equation by evaluating any expressions that involve variables or constants.
  • Isolate the variable by getting rid of any constants or coefficients that are being multiplied by the variable.
  • Check your solution by plugging it back into the original equation.

Conclusion

Solving linear equations can be a challenging task, but with practice and patience, you can become proficient in solving them. By following the steps outlined in this article, you can solve linear equations with ease. Remember to simplify the equation, isolate the variable, and check your solution by plugging it back into the original equation. With these tips and tricks, you will be able to solve linear equations like a pro!