Subtract: $ (3w + 7) - (-4w - 7) $
Understanding the Problem
When dealing with algebraic expressions, it's essential to understand the rules of subtraction and how they apply to variables and constants. In this problem, we're tasked with subtracting one expression from another, which involves combining like terms and simplifying the result.
The Expression to Subtract
The given expression is $ (3w + 7) - (-4w - 7) $. To simplify this expression, we need to apply the rules of subtraction, which state that we can subtract a negative number by changing the sign to positive and then adding the two numbers.
Distributing the Negative Sign
To simplify the expression, we need to distribute the negative sign to the terms inside the parentheses. This means that we'll change the sign of each term inside the parentheses and then combine like terms.
Step 1: Distribute the Negative Sign
When we distribute the negative sign to the terms inside the parentheses, we get:
$ -(3w + 7) = -3w - 7 $
$ -(-4w - 7) = 4w + 7 $
Step 2: Combine Like Terms
Now that we've distributed the negative sign, we can combine like terms. The expression becomes:
$ (3w + 7) - (-4w - 7) = 3w + 7 + 4w + 7 $
Step 3: Simplify the Expression
To simplify the expression, we can combine the like terms by adding their coefficients. In this case, we have:
$ 3w + 4w = 7w $
$ 7 + 7 = 14 $
Step 4: Write the Final Answer
The final answer is obtained by combining the simplified terms:
$ (3w + 7) - (-4w - 7) = 7w + 14 $
Conclusion
In this problem, we applied the rules of subtraction to simplify the given expression. We distributed the negative sign to the terms inside the parentheses, combined like terms, and simplified the expression to obtain the final answer.
Tips and Tricks
- When dealing with algebraic expressions, it's essential to understand the rules of subtraction and how they apply to variables and constants.
- Distributing the negative sign to the terms inside the parentheses can help simplify the expression.
- Combining like terms is a crucial step in simplifying algebraic expressions.
Common Mistakes
- Failing to distribute the negative sign to the terms inside the parentheses.
- Not combining like terms correctly.
- Not simplifying the expression to obtain the final answer.
Real-World Applications
- Algebraic expressions are used in various real-world applications, such as physics, engineering, and economics.
- Understanding the rules of subtraction and how they apply to variables and constants is essential in these fields.
Practice Problems
- Subtract: $ (2x + 5) - (-3x - 5) $
- Subtract: $ (4y - 2) - (-2y + 2) $
- Subtract: $ (6z + 3) - (-2z - 3) $
Solutions
- $ (2x + 5) - (-3x - 5) = 2x + 5 + 3x + 5 = 5x + 10 $
- $ (4y - 2) - (-2y + 2) = 4y - 2 + 2y - 2 = 6y - 4 $
- $ (6z + 3) - (-2z - 3) = 6z + 3 + 2z + 3 = 8z + 6 $
Conclusion
In this article, we discussed how to subtract algebraic expressions by distributing the negative sign to the terms inside the parentheses, combining like terms, and simplifying the expression to obtain the final answer. We also provided tips and tricks, common mistakes, and real-world applications to help readers understand the concept better. Finally, we included practice problems and solutions to help readers practice and reinforce their understanding of the concept.
Understanding the Basics
Subtracting algebraic expressions can be a challenging task, but with the right approach, it can be simplified. In this article, we'll answer some common questions related to subtracting algebraic expressions and provide tips and tricks to help you master this concept.
Q: What is the first step in subtracting algebraic expressions?
A: The first step in subtracting algebraic expressions is to distribute the negative sign to the terms inside the parentheses. This means that you'll change the sign of each term inside the parentheses and then combine like terms.
Q: How do I distribute the negative sign to the terms inside the parentheses?
A: To distribute the negative sign, you'll change the sign of each term inside the parentheses. For example, if you have the expression $ (3x + 5) - (-2x - 3) $, you'll change the sign of each term inside the parentheses to get:
$ -(3x + 5) = -3x - 5 $
$ -(-2x - 3) = 2x + 3 $
Q: What is the next step after distributing the negative sign?
A: After distributing the negative sign, the next step is to combine like terms. This means that you'll add or subtract the coefficients of the like terms to simplify the expression.
Q: How do I combine like terms?
A: To combine like terms, you'll add or subtract the coefficients of the like terms. For example, if you have the expression $ 3x + 2x $, you'll combine the like terms to get:
$ 3x + 2x = 5x $
Q: What are some common mistakes to avoid when subtracting algebraic expressions?
A: Some common mistakes to avoid when subtracting algebraic expressions include:
- Failing to distribute the negative sign to the terms inside the parentheses.
- Not combining like terms correctly.
- Not simplifying the expression to obtain the final answer.
Q: How can I practice subtracting algebraic expressions?
A: You can practice subtracting algebraic expressions by working through practice problems and checking your answers with a calculator or a friend. You can also try creating your own practice problems to challenge yourself.
Q: What are some real-world applications of subtracting algebraic expressions?
A: Subtracting algebraic expressions has many real-world applications, including:
- Physics: Subtracting algebraic expressions is used to calculate the motion of objects and the forces acting on them.
- Engineering: Subtracting algebraic expressions is used to design and optimize systems, such as bridges and buildings.
- Economics: Subtracting algebraic expressions is used to model economic systems and make predictions about future trends.
Q: How can I use technology to help me with subtracting algebraic expressions?
A: You can use technology, such as calculators and computer software, to help you with subtracting algebraic expressions. These tools can help you simplify expressions, solve equations, and graph functions.
Q: What are some tips for mastering subtracting algebraic expressions?
A: Some tips for mastering subtracting algebraic expressions include:
- Practicing regularly to build your skills and confidence.
- Breaking down complex problems into smaller, more manageable parts.
- Using technology to help you simplify expressions and solve equations.
- Seeking help from a teacher or tutor if you're struggling with a particular concept.
Conclusion
In this article, we've answered some common questions related to subtracting algebraic expressions and provided tips and tricks to help you master this concept. By following these tips and practicing regularly, you'll be able to simplify complex expressions and solve equations with ease.