Equivalent expressions and what each form tells you

Answer Key - Grade 7 Math Worksheet - Challenge Me

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

1. 1.

   Kira finds a riddle card tucked in a lunchbox. Which expression is equal to 5(2x − 3) − 4x?

   • 6x − 3
   • 6x − 15
   • -9x
   • 6x + 15
2. 2.

   Luz opens an envelope that holds one tiny puzzle. Luz writes 1.5x + 4.5 = 1.5(x + ?). What number replaces the question mark so the sides are equivalent?

   3
3. 3.

   Noah sharpens a pencil down to a stub for this puzzle. Noah writes 2.5x + 12.5 = 2.5(x + ?). What number replaces the question mark so the sides are equivalent?

   5
4. 4.

   Zee cuts a piece of yarn x cm long and another piece x/2 cm long. Which form shows both pieces together as one multiple of x?

   • x + x/2
   • x/2
   • 3x/2
   • 2x/3
5. 5.

   Jun tests x = 1 on paper: x/2 + 3 and 2x + 1.5 both give 3.5. Jun says they are equivalent. What is wrong with that?

   • They differ at x = 2: x/2 + 3 gives 4 and 2x + 1.5 gives 5.5.
   • 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.
6. 6.

   Kira tests x = 3 on paper: 2(x + 1) and 3x − 1 both give 8. Kira 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 = 3, so they match for every x.
   • They differ at x = 4: 2(x + 1) gives 10 and 3x − 1 gives 11.
7. 7.

   Luz has a rectangle x long and y wide, so the way around is 2x + 2y. What does 2y stand for?

   • one short side
   • the two long sides together, on top and bottom
   • the two short sides together
   • the whole way around
8. 8.

   Milo has a rectangle x long and y wide, so the way around is 2(x + y). What does (x + y) stand for?

   • the number of sides around the rectangle
   • all of the way around
   • half of the way around
   • one long side
9. 9.

   Each level gives Noah x points and costs 3 points to puddles. After 5 levels the total is 5x − 15. What does the 15 stand for?

   • the points lost in one level
   • the number of levels
   • the points lost in all 5 levels
   • the points won in all 5 levels
10. 10.

    Each level gives Pia x points and costs 2 points to puddles. After 6 levels the total is 6(x − 2). What does (x − 2) stand for?

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