Solve For { X $} : : : { 144 = -12x - 60 \}

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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 linear equation, 144 = -12x - 60, and provide a step-by-step guide on how to isolate the variable x.

Understanding Linear Equations

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, and x is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Given Equation

The given equation is 144 = -12x - 60. This equation is a linear equation in one variable, x. Our goal is to isolate the variable x and find its value.

Step 1: Add 60 to Both Sides

To isolate the variable x, we need to get rid of the constant term -60 on the right-hand side of the equation. We can do this by adding 60 to both sides of the equation.

144 = -12x - 60
144 + 60 = -12x - 60 + 60
204 = -12x

Step 2: Divide Both Sides by -12

Now that we have 204 = -12x, we need to get rid of the coefficient -12 on the left-hand side of the equation. We can do this by dividing both sides of the equation by -12.

204 = -12x
\frac{204}{-12} = \frac{-12x}{-12}
-17 = x

Conclusion

In this article, we solved the linear equation 144 = -12x - 60 using algebraic manipulation. We added 60 to both sides of the equation to get rid of the constant term, and then divided both sides by -12 to isolate the variable x. The final answer is x = -17.

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 adding or subtracting numbers, make sure to add or subtract the same value on both sides of the equation.
  • When multiplying or dividing numbers, make sure to multiply or divide the same value on both sides of the equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects, including velocity, acceleration, and distance.
  • Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and structural systems.
  • Economics: Linear equations are used to model economic systems, including supply and demand, cost-benefit analysis, and resource allocation.

Common Mistakes

  • Not following the order of operations (PEMDAS) when solving linear equations.
  • Not adding or subtracting the same value on both sides of the equation.
  • Not multiplying or dividing the same value on both sides of the equation.

Conclusion

Introduction

In our previous article, we provided a step-by-step guide on how to solve the linear equation 144 = -12x - 60. In this article, we will answer some frequently asked questions (FAQs) 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. In other words, it is an equation that can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable x. You can do this by adding or subtracting the same value on both sides of the equation, or by multiplying or dividing the same value on both sides of the equation.

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:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I handle negative numbers when solving linear equations?

A: When solving linear equations, you need to handle negative numbers carefully. When adding or subtracting negative numbers, remember that subtracting a negative number is the same as adding a positive number.

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 concept behind the solution and not just rely on the calculator.

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 adding or subtracting the same value on both sides of the equation
  • Not multiplying or dividing the same value on both sides of the equation
  • Not handling negative numbers correctly

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

A: To check your solution to a linear equation, plug the value of x back into the original equation and see if it's true. If it's true, then your solution is correct.

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

A: Yes, linear equations can be used to solve real-world problems. Linear equations are used in physics, engineering, economics, and many other fields to model and solve problems.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving linear equations and apply them to real-world problems.

Additional Resources

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • Wolfram Alpha: Linear Equations

Practice Problems

  • Solve the linear equation 2x + 5 = 11.
  • Solve the linear equation x - 3 = 7.
  • Solve the linear equation 4x = 24.

Answer Key

  • 2x + 5 = 11: x = 3
  • x - 3 = 7: x = 10
  • 4x = 24: x = 6