4-2 Simplifying Algebraic Expressions
Identify the terms, like terms, coefficients, and constants in each expression.
15. 3a + 2 + 3a + 7
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3a + 2 + 3a + 7 the terms are 3a, 2, 3a, 7; the like terms
are 3a, 3a; the coefficients are 3, 3; and the constants are 2, 7.
16. 4m + 3 + m + 1
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 4m + 3 + m + 1 the terms are 4m, 3, m, 1; the like terms
are 4m, m; the coefficients are 4, 1; and the constants are 3, 1.
17. 3c + 4d + 5c + 8
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3c + 4d + 5c + 8 the terms are 3c, 4d, 5c, 8; the like
terms are 3c, 5c; the coefficients are 3, 4, 5; and the constant is 8.
18. 7j + 11j k + k + 9
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 7j + 11j k + k + 9 the terms are 7j , 11j k , k, 9; there no
like terms; the coefficients are 7, 11, 1; and the constant is 9.
19. 4x + 4y + 4z + 4
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 4x + 4y + 4z + 4 the terms are 4x, 4y, 4z, 4; there are no
like terms; the coefficients are 4, 4, 4; and the constant is 4.
20. 3m + 3n + 2p + 4r
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3m + 3n + 2p + 4r the terms are 3m, 3n, 2p , 4r; there
are no like terms; the coefficients are 3, 3, 2, 4; there are no constants.
Simplify each expression.
21. 4a + 3a
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SOLUTION: 4-2
Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants
are terms
without variables.
So, in the expression 3m + 3n + 2p + 4r the terms are 3m, 3n, 2p , 4r; there
Simplifying
Algebraic
Expressions
are no like terms; the coefficients are 3, 3, 2, 4; there are no constants.
Simplify each expression.
21. 4a + 3a
SOLUTION: 22. 9x + 2x
SOLUTION: 23. –5m + m + 5
SOLUTION: 24. 6x – x + 3
SOLUTION: 25. 7p + 3 + 4p + 5
SOLUTION: 26. 2a + 4 + 2a + 9
SOLUTION: 27. 4a – 3b – 7a – 3b
SOLUTION: 28. –x – 2y – 8x – 2y
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4-2 Simplifying Algebraic Expressions
28. –x – 2y – 8x – 2y
SOLUTION: 29. x + 5(6 + x)
SOLUTION: 30. 2a + 3(2 + a)
SOLUTION: 31. –3(6 – 2r) – 3r
SOLUTION: 32. –2(2x – 5) – 4x
SOLUTION: For each situation write an expression in simplest form that represents the total amount.
33. FASHION
Mateo by
has
y pairs of shoes. His brother has 5 fewer pairs.
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Manual - Powered
Cognero
SOLUTION: total pairs of shoes = number of pairs of shoes Mateo has + number of pairs of shoes Mateo’s brother has
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4-2 Simplifying Algebraic Expressions
For each situation write an expression in simplest form that represents the total amount.
33. FASHION Mateo has y pairs of shoes. His brother has 5 fewer pairs.
SOLUTION: total pairs of shoes = number of pairs of shoes Mateo has + number of pairs of shoes Mateo’s brother has
Let y = number of pairs of shoes Mateo has
Let y – 5 = number of pairs of shoes Mateo’s brother has
So, the expression 2y – 5 represents the total number of pairs of shoes.
34. CELL PHONES You used p minutes one month on your cell phone. The next month you used 75 fewer minutes.
SOLUTION: total minutes = minutes used in one month + minutes used in the next month
Let p = minutes used in one month.
Let p – 75 = minutes used in the next month.
So, the expression 2p – 75 represents the total number of minutes used in two months.
35. SPORTS Nathan scored x points in his first basketball game. He scored three times as many points in his second
game. In his third game, he scored 6 more than the second game.
SOLUTION: total points scored = points scored in first game + points scored in second game + points scored in third game
Let x = points scored in first game.
Let 3x = points scored in second game.
Let 3x + 6 = points scored in third game.
So, the expression 7x + 6 represents the total number of points Nathan scored in his three games.
36. MONEY On Monday, Rebekah spent d dollars on lunch. She spent $0.50 more on Tuesday than she did on
Monday. On Wednesday, she spent twice as much as she did on Tuesday.
SOLUTION: total amount Rebekah spent on lunch = amount spent on Monday + amount spent on Tuesday + amount spent on
Wednesday
Let d = amount Rebekah spent on Monday
Let d + 0.50 = amount Rebekah spent on Tuesday
Let 2(d + 0.50) = amount Rebekah spent on Wednesday
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Let 3x + 6 = points scored in third game.
4-2 Simplifying Algebraic Expressions
So, the expression 7x + 6 represents the total number of points Nathan scored in his three games.
36. MONEY On Monday, Rebekah spent d dollars on lunch. She spent $0.50 more on Tuesday than she did on
Monday. On Wednesday, she spent twice as much as she did on Tuesday.
SOLUTION: total amount Rebekah spent on lunch = amount spent on Monday + amount spent on Tuesday + amount spent on
Wednesday
Let d = amount Rebekah spent on Monday
Let d + 0.50 = amount Rebekah spent on Tuesday
Let 2(d + 0.50) = amount Rebekah spent on Wednesday
So, the expression 4d + $1.50 represents the amount Rebekah spent on lunch on Monday, Tuesday, and Wednesday.
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