Solve: M − 4 = 2 M M - 4 = 2m M − 4 = 2 M .Provide Your Answer Below: M = M = M = □ \square □

by ADMIN 94 views

=====================================================

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific linear equation, m−4=2mm - 4 = 2m, and provide a step-by-step guide on how to arrive at the solution.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation m−4=2mm - 4 = 2m

The given equation is m−4=2mm - 4 = 2m. To solve for mm, we need to isolate the variable on one side of the equation. Let's start by adding 4 to both sides of the equation:

m - 4 + 4 = 2m + 4

This simplifies to:

m = 2m + 4

Isolating the Variable

Now, we need to isolate the variable mm on one side of the equation. To do this, we can subtract 2m2m from both sides of the equation:

m - 2m = 2m - 2m + 4

This simplifies to:

-m = 4

Solving for mm

To solve for mm, we need to get rid of the negative sign in front of the variable. We can do this by multiplying both sides of the equation by -1:

-m × (-1) = 4 × (-1)

This simplifies to:

m = -4

Conclusion

In this article, we solved the linear equation m−4=2mm - 4 = 2m using algebraic manipulation. We started by adding 4 to both sides of the equation, then isolated the variable mm by subtracting 2m2m from both sides. Finally, we solved for mm by multiplying both sides of the equation by -1. The solution to the equation is m=−4m = -4.

Tips and Tricks

  • When solving linear equations, it's essential to isolate the variable on one side of the equation.
  • Use algebraic manipulation to simplify the equation and make it easier to solve.
  • Be careful when multiplying or dividing both sides of the equation by a negative number, as it can change the sign of the variable.

Practice Problems

Try solving the following linear equations:

  1. x+2=3xx + 2 = 3x
  2. y−3=2yy - 3 = 2y
  3. z+1=z+2z + 1 = z + 2

Final Answer

The final answer to the equation m−4=2mm - 4 = 2m is:

m=−4m = \boxed{-4}

=====================================================

Introduction

In our previous article, we solved the linear equation m−4=2mm - 4 = 2m using algebraic manipulation. In this article, we will provide a Q&A guide to help students understand the concept of 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. It can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. 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 when solving a linear equation?

A: When solving a linear equation, you should follow the order of operations (PEMDAS):

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

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

A: When solving a linear equation, you need to be careful when multiplying or dividing both sides of the equation by a negative number. This can change the sign of the variable. For example, if you have the equation −x=2-x = 2, you need to multiply both sides of the equation by -1 to get x=−2x = -2.

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

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

  • Not isolating the variable on one side of the equation.
  • Not following the order of operations.
  • Not handling negative numbers correctly.
  • Not checking your work to make sure the solution is correct.

Q: How do I check my work when solving a linear equation?

A: To check your work when solving a linear equation, you can plug the solution back into the original equation to make sure it is true. For example, if you solve the equation x+2=3xx + 2 = 3x and get x=2x = 2, you can plug x=2x = 2 back into the original equation to get 2+2=3(2)2 + 2 = 3(2), which simplifies to 4=64 = 6. Since this is not true, you know that the solution is incorrect.

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

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

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

Q: How can I practice solving linear equations?

A: There are many ways to practice solving linear equations, including:

  • Working through practice problems in a textbook or online resource.
  • Using online tools and calculators to solve linear equations.
  • Joining a study group or working with a tutor to practice solving linear equations.
  • Creating your own practice problems and solving them on your own.

Final Answer

The final answer to the equation m−4=2mm - 4 = 2m is:

m=−4m = \boxed{-4}