Select the expressions that are equivalent to 3(7q+8)+5.

Question

1) 21q+29
2) 7q+29
3) 29q+21
4) (5q+2q+8)3+5

Answer 1

To simplify the expression \( 3(7q + 8) + 5 \), we can follow these steps:

1. Distribute the 3 inside the parentheses: \[ 3(7q) + 3(8) + 5 = 21q + 24 + 5 \]

2. Combine the constant terms: \[ 21q + 24 + 5 = 21q + 29 \]

Now we have simplified the expression to \( 21q + 29 \).

Now, let's compare it with the given options:

1. \( 21q + 29 \) (This is equivalent to our simplified expression)
2. \( 7q + 29 \) (This is not equivalent)
3. \( 29q + 21 \) (This is not equivalent)
4. \( (5q + 2q + 8)3 + 5 \):
   • Simplifying \( (5q + 2q + 8)3 + 5 \): \[ (7q + 8)3 + 5 = 3(7q) + 3(8) + 5 = 21q + 24 + 5 = 21q + 29 \] (This is also equivalent to our simplified expression)

Thus, the equivalent expressions are:

• 1. \( 21q + 29 \)
• 4. \( (5q + 2q + 8)3 + 5 \)