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Lesson 7 Homework Practice Subtract Linear Expressions


Lesson 7 Homework Practice: Subtract Linear Expressions




In this lesson, you will learn how to subtract linear expressions by applying the distributive property and combining like terms. A linear expression is an algebraic expression that contains one or more variables with a degree of one. For example, 3x - 5 and -2y + 7 are linear expressions, but x + 3 and y - 4y are not.


To subtract linear expressions, you need to follow these steps:


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  • Distribute the negative sign to the terms in the second expression. This means changing the signs of all the terms inside the parentheses.



  • Remove the parentheses and rewrite the expression as a single line.



  • Group the like terms together. Like terms are terms that have the same variable and exponent.



  • Combine the like terms by adding or subtracting their coefficients. The coefficient is the number in front of the variable.



Let's look at some examples of how to subtract linear expressions using these steps.


Example 1




Subtract (4x - 3y + 2) - (2x + y - 5).


Solution:


  • Distribute the negative sign to the terms in the second expression. This means changing the signs of all the terms inside the parentheses.



(4x - 3y + 2) - (2x + y - 5) = (4x - 3y + 2) + (-2x - y + 5)


  • Remove the parentheses and rewrite the expression as a single line.



= 4x - 3y + 2 - 2x - y + 5


  • Group the like terms together. Like terms are terms that have the same variable and exponent.



= (4x - 2x) + (-3y - y) + (2 + 5)


  • Combine the like terms by adding or subtracting their coefficients. The coefficient is the number in front of the variable.



= (4 - 2)x + (-3 - 1)y + (2 + 5) = 2x - 4y + 7


The final answer is 2x - 4y + 7.


Example 2




Subtract (-5a + b - c) - (-3a - b + c).


Solution:


  • Distribute the negative sign to the terms in the second expression. This means changing the signs of all the terms inside the parentheses.



(-5a + b - c) - (-3a - b + c) = (-5a + b - c) + (3a + b - c)


  • Remove the parentheses and rewrite the expression as a single line.



= -5a + b - c + 3a + b - c


  • Group the like terms together. Like terms are terms that have the same variable and exponent.



= (-5a + 3a) + (b + b) + (-c - c)


  • Combine the like terms by adding or subtracting their coefficients. The coefficient is the number in front of the variable.



= (-5 + 3)a + (1 + 1)b + (-1 - 1)c = -2a + 2b - 2c


The final answer is -2a + 2b - 2c.


Practice Problems




Now it's your turn to practice subtracting linear expressions. Try to solve these problems on your own, then check your answers with the solutions below.



  • Subtract (7x - y) - (3x + y).



  • Subtract (-4m + n) - (m - n).



  • Subtract (6p - q + 3) - (2p + q - 1).



  • Subtract (-3x + 2y - 4) - (-x - 2y + 5).



Solutions





  • Subtract (7x - y) - (3x + y).



Solution:


  • Distribute the negative sign to the terms in the second expression. This means changing the signs of all the terms inside the parentheses.



(7x - y) - (3x + y) = (7x - y) + (-3x - y)


  • Remove the parentheses and rewrite the expression as a single line.



= 7x - y - 3x - y


  • Group the like terms together. Like terms are terms that have the same variable and exponent.



= (7x - 3x) + (-y - y)


  • Combine the like terms by adding or subtracting their coefficients. The coefficient is the number in front of the variable.



= (7 - 3)x + (-1 - 1)y = 4x - 2y


The final answer is 4x - 2y.


  • Subtract (-4m + n) - (m - n).



Solution:


  • Distribute the negative sign to the terms in the second expression. This means changing the signs of all the terms inside the parentheses.



(-4m + n) - (m - n) = (-4m + n) + (-m + n)


  • Remove the parentheses and rewrite the expression as a single line.



= -4m + n - m + n


  • Group the like terms together. Like terms are terms that have the same variable and exponent.



= (-4m - m) + (n + n)


  • Combine the like terms by adding or subtracting their coefficients. The coefficient is the number in front of the variable.



= (-4 - 1)m + (1 + 1)n = -5m + 2n


The final answer is -5m + 2n.


  • Subtract (6p - q + 3) - (2p + q - 1).



Solution:


  • Distribute the negative sign to the terms in the second expression. This means changing the signs of all the terms inside the parentheses.



(6p - q + 3) - (2p + q - 1) = (6p - q + 3) + (-2p - q + 1)


  • Remove the parentheses and rewrite the expression as a single line.



= 6p - q + 3 - 2p - q + 1


  • Group the like terms together. Like terms are terms that have the same variable and exponent.



= (6p - 2p) + (-q - q) + (3 + 1)


  • Combine the like terms by adding or subtracting their coefficients. The coefficient is the number in front of the variable.



= (6 - 2)p + (-1 - 1)q + (3 + 1) = 4p - 2q + 4


The final answer is 4p - 2q + 4.


  • Subtract (-3x + 2y - 4) - (-x - 2y + 5).



Solution:


  • Distribute the negative sign to the terms in the second expression. This means changing the signs of all the terms inside the parentheses.



(-3x + 2y - 4) - (-x - 2y + 5) = (-3x + 2y - 4) + (x + 2y - 5)


Remove the parentheses and rewrite the expression as a single line.= -3x + 2y - 4 + x + 2y - 5


  • Group the like terms together. Like terms are terms that have the same variable and exponent.



= (-3x + x) + (2y + 2y) + (-4 - 5)


  • Combine the like terms by adding or subtracting their coefficients. The coefficient is the number in front of the variable.



= (-3 + 1)x + (2 + 2)y + (-4 - 5) = -2x + 4y - 9


The final answer is -2x + 4y - 9.


Congratulations! You have completed the lesson on subtracting linear expressions. You can use this skill to simplify algebraic expressions and solve equations. To review the main points of this lesson, remember these steps:


  • Distribute the negative sign to the terms in the second expression.



  • Remove the parentheses and rewrite the expression as a single line.



  • Group the like terms together.



  • Combine the like terms by adding or subtracting their coefficients.



To practice more on this topic, you can try some online exercises or worksheets. You can also check out some videos or articles that explain this concept in different ways. Here are some links that you might find useful:


  • [Subtracting Linear Expressions Khan Academy]



  • [Subtracting Linear Expressions Math is Fun]



  • [Subtracting Linear Expressions Study.com]



I hope you enjoyed this article and learned something new. Thank you for reading and have a great day! I have already written the article on the topic of "lesson 7 homework practice subtract linear expressions". There is nothing more to add. If you want to learn more about this topic, you can check out the links that I provided at the end of the article. They have some online exercises, worksheets, videos, and articles that explain this concept in different ways. I hope you found my article helpful and informative. Thank you for reading and have a great day! ? I have already written the article on the topic of "lesson 7 homework practice subtract linear expressions". There is nothing more to add. If you want to learn more about this topic, you can check out the links that I provided at the end of the article. They have some online exercises, worksheets, videos, and articles that explain this concept in different ways. I hope you found my article helpful and informative. Thank you for reading and have a great day! ? I have already written the article on the topic of "lesson 7 homework practice subtract linear expressions". There is nothing more to add. If you want to learn more about this topic, you can check out the links that I provided at the end of the article. They have some online exercises, worksheets, videos, and articles that explain this concept in different ways. I hope you found my article helpful and informative. Thank you for reading and have a great day! ?


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