8) $-8 = 2r + 6r$\n10) $4(4 - n) = 4 - 6n$\n12) $-3n - n = -4$\na) $-7$\nb) $4$\nc) $-4$\nd) $1$

8) $-8 = 2r + 6r$\n10) $4(4 - n) = 4 - 6n$\n12) $-3n - n = -4$\na) $-7$\nb) $4$\nc) $-4$\nd) $1$

8) $-8 = 2r + 6r$\n10) $4(4 - n) = 4 - 6n$\n12) $-3n - n = -4$\na) $-7$\nb) $4$\nc) $-4$\nd) $1$

Answer

Explanation:

Step1: Combine like terms

For equation ( - 8=2r + 6r), combine (2r) and (6r) to get (8r). So the equation becomes (-8 = 8r).

Step2: Solve for (r)

Divide both sides of the equation (-8 = 8r) by (8). We have (r=\frac{-8}{8}=-1).

For equation (4(4 - n)=4-6n):

Step1: Expand the left - hand side

Using the distributive property (a(b - c)=ab - ac), where (a = 4), (b = 4), (c=n). So (4(4 - n)=16-4n). The equation becomes (16-4n=4 - 6n).

Step2: Move the terms with (n) to one side

Add (6n) to both sides: (16-4n + 6n=4-6n+6n), which simplifies to (16 + 2n=4).

Step3: Move the constant term to the other side

Subtract (16) from both sides: (16 + 2n-16=4-16), so (2n=-12).

Step4: Solve for (n)

Divide both sides by (2): (n=\frac{-12}{2}=-6).

For equation (-3n - n=-4):

Step1: Combine like terms

Combine (-3n) and (-n) to get (-4n). So the equation is (-4n=-4).

Step2: Solve for (n)

Divide both sides by (-4). We have (n = 1).

Answer:

For ( - 8=2r + 6r), (r=-1). For (4(4 - n)=4-6n), (n=-6). For (-3n - n=-4), the answer is D.