Identifying and Generating Equivalent Algebraic Expressions

Which is an equivalent expression for 30p + 25q - 20?

• 5p(6 + 5q -4)

• 35pq

• 5(6p + 5q -4)

• 5pq(6 + 5 -4)

Select all the expressions that are equivalent to 3x + 9. There are 3 correct answers.

• 3(x + 3)

• 2(x + 4) + (x + 1)

• (x + 5) + 2(x - 2)

• (x + 3) + (x + 3) + (x + 3)

• 3(x + 3) + 2x

Complete the table for each value of k. Are the expressions equivalent?

• 1; 30, 30

  2; 60, 60

  
  

  Yes, the expressions are equivalent.

• 1; 18k + 12, 18k + 12

  2; 36k +12, 36k + 12

  
  

  Yes, the expressions are equivalent.

• 1; 30, 30

  2; 60, 60

  
  

  No, the expressions are not equivalent.

• 1; 18k + 12, 18k + 12

  2; 36k +12, 36k +12

  
  

  No, the expressions are not equivalent.

Select each pair of expressions that are equivalent. There are 3 correct answers.

• 4 + 12x and 4(3x + 1)

• 9x and 2 × 4(x + 1) -1

• 5(x - 1) + (1 - x) and 6x - 4

• 2(x + 1) + (x - 1) and 3x + 1

• 7x + 1/3 - 5x + 1 1/3 and 2x + 1 2/3

Identify an equivalent expression for 3(0.2y - 0.8).

• 3(0.2) - 3(0.8)

• 3.2y - 3.8

• 0.6y - 2.4

• -1.8y

Which of the following expressions are equivalent?

I. 8(j + 3) II. 8j + 24 III. 4(2j + 6)

• I and II only

• I and III only

• II and III only

• I, II, and III

Simplify 2.8(20.5i + 42.3) + (22.2 + 7.5i).

• 57.4i + 42.3 + 22.2 + 7.5i

• 155.3i

• 57.4i + 118.44 + 22.2 + 7.5i

• 140.64 + 64.9i

Bethany earns $10 plus $25 per hour. John performs two tasks per shift and earns $10 plus $10 per hour for one task, and $15 per hour for the other task. At the end of a shift, do Bethany and John earn the same amount?

• Yes, they both earn $10h + $25

• Yes, they both earn $25h + $10.

• No, Bethany earns $10h + $25 and John earns $25h + $10.

• No, Bethany earns $25h +$10 and John earns $10h + $25.

Select all the expressions that are equivalent to 4x + 16. There are 3 correct answers.

• (x + 4) + (3x + 4)

• (3x + 9) + (x + 3)

• 4(x + 4)

• 2(2x + 8)

• 3(x + 5) + x + 1

Complete the table for each value of n. Are the expressions equivalent.

• 1; 8n + 10, 8n + 14

  2; 16n + 20, 16n +28

  
  

  The expressions are equivalent.

• 1; 8n + 20, 8n + 14

  2; 16n + 20, 16n + 28

  
  

  The expressions are not equivalent.

• 1; 28n, 21n

  2; 21n, 23n

  
  

  The expressions are equivalent.

• 1; 28, 22

  2; 36, 30

  
  

  The expressions are not equivalent.