Answer:
The error is located in step 9, because the student made the following operation: [tex](-4)\cdot (-r) = -4\cdot r[/tex], instead of [tex](-4)\cdot (-r) = 4\cdot r[/tex], presented in step 4) of our demonstration. The real solution is 9.
Step-by-step explanation:
First, we proceed to show the appropriate process to solve the equation for [tex]r[/tex] by algebraic means. That is:
1) [tex]-4\cdot (6-r) = 12[/tex] Given
2) [tex](-4)\cdot [6+(-r)] = 12[/tex] Definition of substraction
3) [tex](-4)\cdot (6) +(-4)\cdot (-r) = 12[/tex] Distributive property
4) [tex](-24) +4\cdot r = 12[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]/[tex](-a)\cdot (-b) = a\cdot b[/tex]
5) [tex]4\cdot r +[24+(-24)] = 12 +24[/tex] Compatibility with addition/Commutative and associative properties
6) [tex]4\cdot r = 36[/tex] Existence of additive inverse/Modulative property
7) [tex]r\cdot (4\cdot 4^{-1}) = 36\cdot 4^{-1}[/tex] Compatibility with multiplication/Commutative and associative properties
8) [tex]r = 9[/tex] Existence of multiplicative inverse/Definition of division/Result
The error is located in step 9, because the student made the following operation: [tex](-4)\cdot (-r) = -4\cdot r[/tex], instead of [tex](-4)\cdot (-r) = 4\cdot r[/tex], presented in step 4) of our demonstration. The real solution is 9.
