Justify your answer with a model, color (reds \& blues) or an explanation. 6) \( 5+3(-4)^{\text {tinnogeren }} 71 \) 12b-(-1b) 8) \( 5(-3 m-6) \) 9) \( \cdot 2(6+8) \) zgId 11) \( 4 n-(n+6) \) 12) \( 8(k-3)+4 k \) bns 279 13) \( -7 c+5 a+2+8 a+10 c-8 \) 14) \( 5 p+5 m-6-5 p+10 m-10 \) 15) Enter the value of a to the expression \( (5 y+8)+(6 y-9) \) is equivalent to \( (n y-1) \). 16) Enter the value of \( p \) so that the expression \( 5(3+n) \) is equivalent to \( 5(n+p) \).

Let's break down each of the problems step by step, extracting the known conditions and solving them logically. ### Problem 6: **Expression:** \( 5 + 3(-4)^{\text{tinnogeren}} + 71 + 12b - (-1b) \) 1. **Simplify the expression:** - The term \( -(-1b) \) simplifies to \( +1b \). - Combine like terms: \( 5 + 71 = 76 \) and \( 12b + 1b = 13b \). - The expression becomes \( 76 + 3(-4)^{\text{tinnogeren}} + 13b \). ### Problem 8: **Expression:** \( 5(-3m - 6) \) 1. **Distribute the 5:** - \( 5 \cdot -3m = -15m \) - \( 5 \cdot -6 = -30 \) - The expression simplifies to \( -15m - 30 \). ### Problem 9: **Expression:** \( \cdot 2(6 + 8) \) 1. **Calculate inside the parentheses:** - \( 6 + 8 = 14 \) - The expression becomes \( 2 \cdot 14 = 28 \). ### Problem 11: **Expression:** \( 4n - (n + 6) \) 1. **Distribute the negative sign:** - \( 4n - n - 6 \) - Combine like terms: \( 4n - n = 3n \). - The expression simplifies to \( 3n - 6 \). ### Problem 12: **Expression:** \( 8(k - 3) + 4k \) 1. **Distribute the 8:** - \( 8k - 24 + 4k \) - Combine like terms: \( 8k + 4k = 12k \). - The expression simplifies to \( 12k - 24 \). ### Problem 13: **Expression:** \( -7c + 5a + 2 + 8a + 10c - 8 \) 1. **Combine like terms:** - Combine \( 5a + 8a = 13a \). - Combine \( -7c + 10c = 3c \). - Combine constants: \( 2 - 8 = -6 \). - The expression simplifies to \( 3c + 13a - 6 \). ### Problem 14: **Expression:** \( 5p + 5m - 6 - 5p + 10m - 10 \) 1. **Combine like terms:** - The \( 5p \) and \( -5p \) cancel out. - Combine \( 5m + 10m = 15m \). - Combine constants: \( -6 - 10 = -16 \). - The expression simplifies to \( 15m - 16 \). ### Problem 15: **Expression:** \( (5y + 8) + (6y - 9) \) is equivalent to \( (ny - 1) \). 1. **Combine like terms:** - Combine \( 5y + 6y = 11y \). - Combine constants: \( 8 - 9 = -1 \). - The expression simplifies to \( 11y - 1 \). - Set \( ny - 1 = 11y - 1 \) to find \( n \). - Thus, \( n = 11 \). ### Problem 16: **Expression:** \( 5(3 + n) \) is equivalent to \( 5(n + p) \). 1. **Distribute the 5:** - \( 5 \cdot 3 + 5n = 15 + 5n \). - The expression becomes \( 15 + 5n = 5n + 5p \). - Set \( 15 = 5p \) to find \( p \). - Thus, \( p = 3 \). ### Summary of Results: - Problem 6: \( 76 + 3(-4)^{\text{tinnogeren}} + 13b \) - Problem 8: \( -15m - 30 \) - Problem 9: \( 28 \) - Problem 11: \( 3n - 6 \) - Problem 12: \( 12k - 24 \) - Problem 13: \( 3c + 13a - 6 \) - Problem 14: \( 15m - 16 \) - Problem 15: \( n = 11 \) - Problem 16: \( p = 3 \)