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?

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

   Milo puts on glasses to read very tiny print. Milo writes 0.5x + 3.5 = 0.5(x + ?). What number replaces the question mark so the sides are equivalent?

   7
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.

   Ari mixes paint: x/2 liter of blue and 3/4 liter of white. Which form shows the whole mix as one fraction over 4?

   • (2x + 3)/4
   • 5x/4
   • (x + 3)/4
   • x/2 + 3/4
6. 6.

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

   • They differ at x = 0: 2x + 3 gives 3 and 3x + 4 gives 4.
   • Nothing. They match at x = -1, so they match for every x.
   • One test with a bigger number would prove they are equivalent.
   • Nothing. Both are linear, so they are equivalent.
7. 7.

   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?

   • 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 = 2: x/2 + 3 gives 4 and 2x + 1.5 gives 5.5.
   • Nothing. Both are linear, so they are equivalent.
8. 8.

   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?

   • Nothing. Both are linear, so they are equivalent.
   • They differ at x = 4: 2(x + 1) gives 10 and 3x − 1 gives 11.
   • Nothing. They match at x = 3, so they match for every x.
   • One test with a bigger number would prove they are equivalent.
9. 9.

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

   • the whole way around
   • one short side
   • the two short sides together
   • the two long sides together, on top and bottom
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 lost in one level
    • the number of levels
    • the points from one level