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.

   Jun cuts a puzzle card out with scissors. Which expression is equal to 3(x + 2) + 2x − 4?

   • 5x + 2
   • 4x + 2
   • 5x − 2
   • 7x
2. 2.

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

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

   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
4. 4.

   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
5. 5.

   Pia copies a puzzle onto paper, then doodles a cat in the corner. Pia writes x/2 + 5/2 = (x + ?)/2. What number replaces the question mark so the sides are equivalent?

   5
6. 6.

   Ren spots a puzzle at the back of a book. Ren writes x/3 + 4/3 = (x + ?)/3. What number replaces the question mark so the sides are equivalent?

   4
7. 7.

   Tala has one minute on the clock, and it ticks loudly. Tala writes x/4 + 3/2 = (x + ?)/4. What number replaces the question mark so the sides are equivalent?

   6
8. 8.

   Esme tests x = -1 on paper: 2x + 3 and 3x + 4 both give 1. Esme says they are equivalent. What is wrong with that?

   • Nothing. They match at x = -1, so they match for every x.
   • One test with a bigger number would prove they are equivalent.
   • They differ at x = 0: 2x + 3 gives 3 and 3x + 4 gives 4.
   • Nothing. Both are linear, so they are equivalent.
9. 9.

   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?

   • They differ at x = 4: 2(x + 1) gives 10 and 3x − 1 gives 11.
   • Nothing. Both are linear, so they are equivalent.
   • One test with a bigger number would prove they are equivalent.
   • Nothing. They match at x = 3, so they match for every x.
10. 10.

    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 whole way around
    • the two short sides together