Question

Can someone please help me

Answer 1

The error is located in step 9, because the student made the following operation:
`(-4)\cdot (-r) = -4\cdot r`, instead of
`(-4)\cdot (-r) = 4\cdot r`, presented in step 4) of our demonstration. The real solution is 9.

Explanation:

First, we proceed to show the appropriate process to solve the equation for
`r` by algebraic means. That is:

1)
`-4\cdot (6-r) = 12` Given

2)
`(-4)\cdot [6+(-r)] = 12` Definition of substraction

3)
`(-4)\cdot (6) +(-4)\cdot (-r) = 12` Distributive property

4)
`(-24) +4\cdot r = 12`
`(-a)\cdot b = -a\cdot b`/
`(-a)\cdot (-b) = a\cdot b`

5)
`4\cdot r +[24+(-24)] = 12 +24` Compatibility with addition/Commutative and associative properties

6)
`4\cdot r = 36` Existence of additive inverse/Modulative property

7)
`r\cdot (4\cdot 4^(-1)) = 36\cdot 4^(-1)` Compatibility with multiplication/Commutative and associative properties

8)
`r = 9` Existence of multiplicative inverse/Definition of division/Result

The error is located in step 9, because the student made the following operation:
`(-4)\cdot (-r) = -4\cdot r`, instead of
`(-4)\cdot (-r) = 4\cdot r`, presented in step 4) of our demonstration. The real solution is 9.