Let’s analyze Lorena’s work step by step:
The original equation is:
\[ 5k - 3(2k - 2) - 9 = 0 \]
Step 1: Distributing -3
- Lorena writes: \(5k - 6k + 2 - 9 = 0\)
The correct distribution of \(-3(2k - 2)\) is \(-6k + 6\), not \(-6k + 2\). This means that her distribution step is incorrect.
Step 2: Combining like terms
- Lorena represents the equation as \(-k - 7 = 0\)
Since the previous step was incorrect, combining the terms is also incorrect. The correct combination of terms after proper distribution should result in a different equation.
Step 3: Isolating the variable term
- In her work, she moves from \(-k - 7 = 0\) to \(-k = 7\).
Since her previous steps were wrong, this step is also incorrect because it follows from the incorrect working equation.
Step 4: Multiplying or isolating the variable
- She states that she isolated k correctly, but since the previous equations were wrong, this statement does not hold.
Finally, since her isolating method and each step stemmed from a miscalculation in distributing and combining like terms, Lorena did not find the correct solution.
Based on these analyses, we can conclude:
- In Step 1, she correctly distributed –3 to the parentheses. - False
- In Step 2, she combined like terms 5k and 2k. - False (Even if we assume she combined correctly, the terms were already incorrect.)
- In Step 3, she applied the multiplication property of equality to isolate the variable term. - False
- In Step 4, she should have multiplied both sides by –1 to isolate the variable. - True (this is generally the approach, but since her earlier steps are incorrect, this statement in the context of her work cannot be confirmed.)
- Lorena found the correct solution to the linear equation. - False
Thus, none of the statements apply as correct from the options given.