Find Equivalent Expressions to 9y+4x+35: Multiple Choice Challenge

Let's simplify each expression option and compare them with the original expression $9y + 4x + 35$:

a. $3y + 2x + 6y + 30 + 7$

• Combine like terms:
  $3y + 6y = 9y$ and $2x$, $30 + 7 = 37$.
• The expression becomes: $9y + 2x + 37$, which is not equivalent to the original.

b. $5y + 3x + 4y + 30 + x + 5$

• Combine like terms:
  $5y + 4y = 9y$, $3x + x = 4x$, $30 + 5 = 35$.
• The expression becomes: $9y + 4x + 35$, which matches the original expression.

c. $4x + 30 + 9y + 5$

• Rearrange and combine constants:
  $4x + 9y + (30 + 5 = 35)$.
• The expression becomes: $9y + 4x + 35$, which matches the original expression.

d. $3(3y + 10) + 5 + 2 \cdot 2x$

• Distribute and simplify:
  $3 \cdot 3y = 9y$, $3 \cdot 10 = 30$, $5$, $2 \cdot 2x = 4x$.
• The expression becomes: $9y + 30 + 5 + 4x = 9y + 4x + 35$, which matches the original expression.

e. $5(8 + x) - x + 3y \cdot 3y - 5$

• Distribute and simplify:
  $5 \cdot 8 = 40$, $5 \cdot x = 5x$, $-x$, and $3y \cdot 3y = 9y^2$.
• The expression becomes: $40 + 5x - x + 9y^2 - 5$.
• Arrange: $4x + 9y^2 + 35$, which does not match the original expression.

f. $2x \cdot 2 + 3(2y + 10) + 5 + 3y$

• Distribute and simplify:
  $2x \cdot 2 = 4x$, $3 \cdot 2y = 6y$, $3 \cdot 10 = 30$, $5$, and $3y$.
• The expression becomes: $4x + 6y + 3y + 30 + 5$.
• Combine like terms:
  $6y + 3y = 9y$.
• The expression simplifies to $9y + 4x + 35$, which matches the original expression.

Therefore, the expressions a, e do not match the original, while b, c, d, and f do, confirming these are equivalent to $9y + 4x + 35$.

The correct answer is b. c. d. f.