Question

extended practice
intro to algebraic expressions

1. circle each of the terms in the expression.

2x + 3y + 10 - x - 2y - 4.

1. circle each expression and box each equation.

5 3x 5 + 7 = 20 - 8 y + 7 5 + 10 = 35 + 14 =

1. identify the coefficients, constants, and variables in the expression 5x + 8y + 7 - 3x - y + 9.
2. identify the like terms in each expression:

a. 10 + 3x + 5 - x
b. 5c + 3d + 11c - 3

1. simplify each expression.

a. 8x + 4x + 5 - 2
b. 5y + 10 + 9y - 2x

1. simplify each expression.

a. 5x + 10 - x + 7
b. 18a + 6m + 9 - 13a - 3m + 11

1. which expression has more terms? explain how you know.

a + 2b + 3c + 4d + 5
a + (b + b) + (c + c + c) + (d + d + d + d) + (1 + 1 + 1 + 1 + 1)

Explanation:

Step1: Identify terms in 2x + 3y + 10 - x - 2y - 4

Terms are 2x, 3y, 10, -x, -2y, -4.

Step2: Categorize expressions and equations in 5, 3x, 5 + 7 = 20 - 8, y + 7, 5 + 10 =, 35 + 14 =

Expressions: 5, 3x, y + 7. Equations: 5 + 7 = 20 - 8. Note 5 + 10 = and 35 + 14 = are incomplete equations.

Step3: Identify coefficients, constants and variables in 5x + 8y + 7 - 3x - y + 9

Coefficients: 5, 8, -3, -1. Constants: 7, 9. Variables: x, y.

Step4: Identify like - terms in 10 + 3x + 5 - x

Like - terms are 10 and 5 (constants), 3x and -x (x - terms). In 5c + 3d + 11c - 3, like - terms are 5c and 11c (c - terms).

Step5: Simplify 8x + 4x + 5 - 2

Combine like - terms: (8x+4x)+(5 - 2)=12x + 3. In 5y + 10 + 9y - 2x, combine like - terms: (5y + 9y)-2x + 10=14y-2x + 10.

Step6: Simplify 5x + 10 - x + 7

Combine like - terms: (5x - x)+(10 + 7)=4x+17. In 18a + 6m + 9 - 13a - 3m + 11, combine like - terms: (18a - 13a)+(6m - 3m)+(9 + 11)=5a + 3m+20.

Step7: Compare number of terms in a + 2b + 3c + 4d + 5 and a+(b + b)+(c + c + c)+(d + d + d + d)+(1 + 1 + 1 + 1 + 1)

The first expression has 5 terms. The second expression, when expanded, also has 5 terms. They have the same number of terms.

Answer:

1. Terms: 2x, 3y, 10, -x, -2y, -4
2. Expressions: 5, 3x, y + 7; Equation: 5 + 7 = 20 - 8
3. Coefficients: 5, 8, -3, -1; Constants: 7, 9; Variables: x, y
4. a. 10 and 5, 3x and -x; b. 5c and 11c
5. a. 12x + 3; b. 14y-2x + 10
6. a. 4x+17; b. 5a + 3m+20
7. They have the same number of terms (5 terms each)