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.

   In each level, Tala wins x points from stars and loses 4 points to puddles. There are 6 levels. Which expression for all the levels shows the points from one level?

   • 6(x − 4)
   • 6x − 24
   • -18x
   • 6x − 4
2. 2.

   Each of Zee's 4 boxes holds x pencils and 3 erasers, so the total is 4x + 12. What does the 12 stand for?

   • the erasers in one box
   • the erasers in all 4 boxes
   • the pencils in all 4 boxes
   • the number of boxes
3. 3.

   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 number of packs
   • the stickers in one pack
   • the crayons and stickers in one pack
   • the crayons and stickers in all 6 packs
4. 4.

   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 all 3 buckets
   • the pebbles in one bucket
   • the shells in all 3 buckets
   • the number of buckets
5. 5.

   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 lost in one level
   • the number of levels
   • the points from all 4 levels
   • the points from one level
6. 6.

   Milo solves a puzzle on the bus, bumps and all. Milo writes 3.5x + 14 = 3.5(x + ?). What number replaces the question mark so the sides are equivalent?

   4
7. 7.

   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
8. 8.

   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
9. 9.

   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. Both are linear, so they are equivalent.
   • Nothing. They match at x = 1, so they match for every x.
   • They differ at x = 2: 2x + 6 gives 10 and 3x + 5 gives 11.
10. 10.

    Ari tests x = 2 on paper: 3x + 4 and 2x + 6 both give 10. Ari says they are equivalent. What is wrong with that?

    • One test with a bigger number would prove they are equivalent.
    • Nothing. Both are linear, so they are equivalent.
    • They differ at x = 3: 3x + 4 gives 13 and 2x + 6 gives 12.
    • Nothing. They match at x = 2, so they match for every x.