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, Pia wins x points from stars and loses 3 points to puddles. There are 4 levels. Which expression for all the levels shows the points from one level?

   • 4x − 3
   • 4(x − 3)
   • -8x
   • 4x − 12
2. 2.

   In each level, Ren wins x points from stars and loses 2 points to puddles. There are 5 levels. Which expression counts the points from stars and the points lost separately, for all the levels?

   • -5x
   • 5(x − 2)
   • 5x − 2
   • 5x − 10
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 crayons and stickers in all 6 packs
   • the number of packs
   • the crayons and stickers in one pack
   • the stickers in one pack
4. 4.

   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 number of levels
   • the points from all 4 levels
   • the points lost in one level
   • the points from one level
5. 5.

   Jun turns on a lamp for the late puzzle. Jun writes -2x − 10 = -2(x + ?). What number replaces the question mark so the sides are equivalent?

   5
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.

   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
8. 8.

   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
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?

   • 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.
   • One test with a bigger number would prove they are equivalent.
   • Nothing. Both are linear, so they are equivalent.
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?

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