Equivalent expressions and what each form tells you

Answer Key - Grade 7 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Each of Ari's 6 packs holds x crayons and 3 stickers, so the total is 6(x + 3). What does (x + 3) stand for?

   • the crayons and stickers in one pack
   • the crayons and stickers in all 6 packs
   • the stickers in one pack
   • the number of packs
2. 2.

   Each of Bo's 3 buckets holds x shells and 5 pebbles, so the total is 3x + 15. What does the 15 stand for?

   • the pebbles in one bucket
   • the pebbles in all 3 buckets
   • the shells in all 3 buckets
   • the number of buckets
3. 3.

   Each level gives Esme x points and costs 5 points to puddles. After 4 levels the total is 4(x − 5). What does (x − 5) stand for?

   • the points from one level
   • the points lost in one level
   • the points from all 4 levels
   • the number of levels
4. 4.

   Kira reads a puzzle painted on a castle wall. Kira writes 2.5x + 10 = 2.5(x + ?). What number replaces the question mark so the sides are equivalent?

   4
5. 5.

   Luz reads a puzzle by flashlight in a tent. Luz writes -3x + 12 = -3(x + ?). What number replaces the question mark so the sides are equivalent?

   -4
6. 6.

   Noah finds a puzzle on top of the piano. Noah writes 5(x − 4) = 5x − ?. What number replaces the question mark so the sides are equivalent?

   20
7. 7.

   Pia ties a puzzle card to a kite. Pia writes 1.5(x + 6) = 1.5x + ?. What number replaces the question mark so the sides are equivalent?

   9
8. 8.

   Ren gets a puzzle from a toy rocket. Ren writes -3(x + 2) = -3x + ?. What number replaces the question mark so the sides are equivalent?

   -6
9. 9.

   Tala finds a puzzle under the plate. Tala writes 3.5(x + 2) = 3.5x + ?. What number replaces the question mark so the sides are equivalent?

   7
10. 10.

    Zee tests x = 1 on paper: 2x + 6 and 3x + 5 both give 8. Zee says they are equivalent. What is wrong with that?

    • One test with a bigger number would prove they are equivalent.
    • Nothing. They match at x = 1, so they match for every x.
    • Nothing. Both are linear, so they are equivalent.
    • They differ at x = 2: 2x + 6 gives 10 and 3x + 5 gives 11.