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.

   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
5. 5.

   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
6. 6.

   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
7. 7.

   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?

   • 3x/2
   • x + x/2
   • x/2
   • 2x/3
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?

   • 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.
   • Nothing. They match at x = -1, so they match for every x.
9. 9.

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

   • all of the way around
   • the number of sides around the rectangle
   • one long side
   • half of the way around
10. 10.

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