Find the midpoint of side EF.

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.

Step-by-step 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.

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3 years ago