Given: -8(x-3)=-32 Prove: x=7

Question

I need four statements and reasons.

Answer 1

-8(x-3)=-32

 

-8x+24=-32    distributive property

-8x+24+(-24)=-32+(-24)    addition property of equality

-8x+0=-56    property of opposites, or, additive inverses (a number plus its opposite equals zero); also, for the right-hand side its the definition of addition of two negative integers

-8x=-56    additive identity property, or, additive property of zero (any number plus zero equals that number)

(-1/8)(-8x)=(-1/8)(-56)    multiplication property of equality

 1x=7  multiplicative inverse property for the left side (a*[1/a]=1 and definition of multiplication of numbers for the right side

  x=7  multiplicative identity property  (1*a=a and 1x=x)

 I have more than four statements so you can leave it like it is or change it accordingly, but there are really more than four concepts involved.