Identify the pair of equivalent expressions.

Question

3x + 12 and 3 (x + 4)

-2 (x + 2) and -2 +4

3x + 4x and x^2 (3 + 4)

3 (x + 2) and 3x + 5

Answer 1

To identify the pair of equivalent expressions, we will simplify each option:

1. 3x + 12 and 3(x + 4)

   • Simplifying 3(x + 4):
     \(3(x + 4) = 3x + 12\)
   • These expressions are equivalent.

2. -2(x + 2) and -2 + 4

   • Simplifying -2(x + 2):
     \(-2(x + 2) = -2x - 4\)
   • The second expression simplifies to 2.
   • These expressions are not equivalent.

3. 3x + 4x and x^2(3 + 4)

   • Simplifying 3x + 4x:
     \(3x + 4x = 7x\)
   • Simplifying x^2(3 + 4):
     \(x^2(3 + 4) = 7x^2\)
   • These expressions are not equivalent.

4. 3(x + 2) and 3x + 5

   • Simplifying 3(x + 2):
     \(3(x + 2) = 3x + 6\)
   • These expressions are not equivalent.

The only pair of equivalent expressions is 3x + 12 and 3(x + 4).