Select The Correct Answer.Which Equation Is Equivalent To The Given Equation? 7 M + 11 = − 4 ( 2 M + 3 7m + 11 = -4(2m + 3 7 M + 11 = − 4 ( 2 M + 3 ]A. − M = 1 -m = 1 − M = 1 B. − 15 M = − 23 -15m = -23 − 15 M = − 23 C. − M = − 1 -m = -1 − M = − 1 D. 15 M = − 23 15m = -23 15 M = − 23

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 type of linear equation, which is equivalent to the given equation $7m + 11 = -4(2m + 3)$. We will explore the different methods of solving this equation and provide step-by-step solutions to help students understand the concept better.

Understanding the Given Equation

The given equation is $7m + 11 = -4(2m + 3)$. To solve this equation, we need to follow the order of operations (PEMDAS) and simplify the expression.

Step 1: Distribute the Negative 4

The first step is to distribute the negative 4 to the terms inside the parentheses.

-4(2m + 3) = -8m - 12

Step 2: Rewrite the Equation

Now, we can rewrite the equation by substituting the simplified expression.

7m + 11 = -8m - 12

Step 3: Add 8m to Both Sides

To isolate the variable m, we need to add 8m to both sides of the equation.

7m + 8m + 11 = -8m + 8m - 12

Step 4: Simplify the Equation

Now, we can simplify the equation by combining like terms.

15m + 11 = -12

Step 5: Subtract 11 from Both Sides

To further isolate the variable m, we need to subtract 11 from both sides of the equation.

15m + 11 - 11 = -12 - 11

Step 6: Simplify the Equation

Now, we can simplify the equation by combining like terms.

15m = -23

Selecting the Correct Answer

Now that we have solved the equation, we can select the correct answer from the options provided.

Option A: $-m = 1$

This option is incorrect because we have not isolated the variable m to the left-hand side of the equation.

Option B: $-15m = -23$

This option is incorrect because we have not multiplied both sides of the equation by -1.

Option C: $-m = -1$

This option is incorrect because we have not isolated the variable m to the left-hand side of the equation.

Option D: $15m = -23$

This option is correct because we have solved the equation and isolated the variable m to the left-hand side of the equation.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the order of operations and simplifying the expression, we can solve equations like $7m + 11 = -4(2m + 3)$. In this article, we have provided a step-by-step solution to help students understand the concept better. We have also selected the correct answer from the options provided, which is $15m = -23$.

Tips and Tricks

• Always follow the order of operations (PEMDAS) when solving linear equations.
• Simplify the expression by combining like terms.
• Isolate the variable to the left-hand side of the equation.
• Check your answer by plugging it back into the original equation.

Practice Problems

Try solving the following linear equations:

1. $2x + 5 = 3(x - 2)$
2. $x - 3 = 2(x + 1)$
3. $4y + 2 = -3(y - 1)$

Answer Key

1. $x = 1$
2. $x = -5$
3. $y = -1$

References

• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f8f7d1/x2f8f7d2
• [2] Mathway. (n.d.). Linear Equations. Retrieved from https://www.mathway.com/subjects/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 is a simple equation that can be solved using basic algebraic operations.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

1. Simplify the expression by combining like terms.
2. Isolate the variable to the left-hand side of the equation.
3. Check your answer by plugging it back into the original equation.

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. The acronym PEMDAS stands for:

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 simplify an expression?

A: To simplify an expression, combine like terms by adding or subtracting the coefficients of the same variables.

Q: What is a like term?

A: A like term is a term that has the same variable(s) with the same exponent(s).

Q: How do I isolate a variable?

A: To isolate a variable, perform the necessary operations to get the variable by itself on one side 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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

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

A: Yes, you can use a calculator to solve a linear equation, but it's always a good idea to check your answer by plugging it back into the original equation.

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 simplifying the expression
• Not isolating the variable
• Not checking the answer

Q: How do I check my answer?

A: To check your answer, plug it back into the original equation and make sure it is true.

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

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

• Physics: to describe the motion of objects
• Engineering: to design and optimize systems
• Economics: to model economic systems
• Computer Science: to solve problems in computer programming

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article, you can become proficient in solving linear equations and apply them to a variety of problems. Remember to always follow the order of operations (PEMDAS), simplify the expression, isolate the variable, and check your answer.