13. $-(5a + 6)=2(3a + 8)$\n15. $3w - 6+2w=-2 + w$\n17. $14 + 3n=8n-3(n - 4)$

Explanation:

Step1: Solve equation 13

First, distribute on both sides. [-(5a + 6)=-5a - 6] and [2(3a + 8)=6a+16]. So the equation becomes (-5a - 6=6a + 16). Add (5a) to both sides: (-6=6a + 5a+16), which simplifies to (-6 = 11a+16). Subtract 16 from both sides: (-6-16=11a), so (-22 = 11a). Divide both sides by 11: (a=\frac{-22}{11}=-2).

Step2: Solve equation 15

Combine like - terms on the left - hand side: (3w+2w-6=-2 + w), so (5w-6=-2 + w). Subtract (w) from both sides: (5w - w-6=-2), which gives (4w-6=-2). Add 6 to both sides: (4w=-2 + 6), so (4w = 4). Divide both sides by 4: (w=\frac{4}{4}=1).

Step3: Solve equation 17

First, distribute on the right - hand side: (-3(n - 4)=-3n+12). So the equation (14 + 3n=8n-3n + 12). Combine like - terms on the right - hand side: (14 + 3n=5n+12). Subtract (3n) from both sides: (14=5n-3n + 12), which simplifies to (14 = 2n+12). Subtract 12 from both sides: (14-12=2n), so (2 = 2n). Divide both sides by 2: (n=\frac{2}{2}=1).

Answer:

For equation 13, (a=-2). For equation 15, (w = 1). For equation 17, (n = 1).