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.

   Esme finds a puzzle taped to the door. Which expression is equal to 2(3x − 1) + x + 5?

   • 7x + 4
   • 10x
   • 7x + 7
   • 7x + 3
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.

   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
4. 4.

   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
5. 5.

   Bo builds a kite frame with two sides of x cm and two sides of y cm. Which form of the whole way around shows half of it inside one set of parentheses?

   • x + y
   • 2x + 2y
   • 2x + y
   • 2(x + y)
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?

   • 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.
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?

   • 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.
   • Nothing. They match at x = 1, so they match for every x.
   • One test with a bigger number would prove they are equivalent.
8. 8.

   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
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 won in all 5 levels
   • the points lost in one level
   • the number of levels
   • the points lost 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 lost in one level
    • the points from all 6 levels
    • the number of levels
    • the points from one level