2. which equation is equivalent to the equation below?
5(n + 6) = 2(n-3) +4
a. 5n + 6 = 2n +1
b. 5n + 30 = 2n - 2
c. 5n +6=2n - 2
d. in + 30 = 2n +1

  b.  5n + 30 = 2n - 2

Step-by-step explanation:

The distributive property requires the outside factor be applied to every term inside parentheses. After eliminating parentheses using the distributive property, terms can be collected on the right.

  5(n +6) = 2(n -3) +4

  5n +5·6 = 2n +2(-3) +4

  5n + 30 = 2n -6 +4

  5n + 30 = 2n - 2 . . . . . matches choice B

i think that you should ask google for the answer to that problem because if we don't know it google does

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.