Question

1.) -4(n-7)+4n=-8-3(n-5)

2.) 4(-8n+10)+4(4n-4)=-6n+2n

Answer 1

1) n = - 7 2) n = 2

Explanation:

1)

-4(n-7)+4n=-8-3(n-5) Let's multiply it out

-4*n - 4* (-7) + 4n = - 8 - 3*n -3 * (- 5)

-4n + 28 + 4n = - 8 -3n +15 Combine like terms

-4n + 4n + 28 = -8 + 15 - 3n

28 = 7 - 3n Subtract 7 from each side

28 - 7 = 7 - 7 - 3n

21 = - 3n Divide each side by -3

21 / -3 = - 3n / -3 -3 cancels on the right

21 / -3 = n

- 7 = n

2)

4(-8n+10)+4(4n-4)= -6n+2n Multiply it out

4 * - 8n + 4 * 10 + 4 * 4n + 4 * (-4) = - 6n + 2n

- 32n + 40 + 16n - 16 = - 6n + 2n Combine like terms

- 32n + 16n + 40 - 16 = - 6n + 2n

- 16n + 24 = - 4n Add 16n to each side

- 16n + 16n + 24 = - 4n + 16n

24 = 12n Divide each side by 12

24/12 = 12n/12 12 cancels on the right

24/12 = n

2 = n

Answer 2

`\huge\boxed{1)\ n=-7}\\\boxed{2)\ n=2}`

Explanation:

`1)\\-4(n-7)+4n=-8-3(n-5)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\(-4)(n)+(-4)(-7)+4n=-8+(-3)(n)+(-3)(-5)\\\\-4n+28+4n=-8-3n+15\\\\\text{combine like terms}\\\\(-4n+4n)+28=-3n+(-8+15)\\\\28=-3n+7\\\\\text{subtract 7 from both sides}\\\\28-7=-3n+7-7\\\\21=-3n\\\\\text{divide both sides by (-3)}\\\\(21)/(-3)=(-3n)/(-3)\\\\-7=n\to\boxed{n=-7}`

`2)\\4(-8n+10)+4(4n-4)=-6n+2n\\\\\text{use the distributive property}\\\\(4)(-8n)+(4)(10)+(4)(4n)+(4)(-4)=-6n+2n\\\\-32n+40+16n-16=-6n+2n\\\\\text{combine like terms}\\\\(-32n+16n)+(40-16)=(-6n+2n)\\\\-16n+24=-4n\\\\\text{add}\ 16n\ \text{to both sides}\\\\-16n+16n+24=-4n+16n\\\\24=12n\\\\\text{divide both sides by 12}\\\\(24)/(12)=(12n)/(12)\\\\2=n\to\boxed{n=2}`