Question

Lorena solved the equation 5k - 3 ( 2k - 2/3 ) - 9 = 0. Her steps are below.

1. 5k - 6k + 2 - 9 = 0
2. -k - 7 = 0
3. -k = 7
4. k = 1
Ana Lorena’sena’s work to determine which statements are correct.
In Step 1, she correctly distributed -3 to the parentheses.
In Step 2, she combined like terms 5k and 2k.
In Step 3, she applied the multiplication property of equality to isolate the variable term.
In Step 4, she should have multiplied both sides by -1 to isolate the variable.
Lorena found the correct solution to the linear equation.
I am a little confused on which ones are right and need some help."

Answer 1

Lorena correctly distributed and combined like terms in Step 1 of the equation 5k - 3 ( 2k - 2/3 ) - 9 = 0. She then used the multiplication property of equality in Step 3 to isolate the variable. In Step 4, she simplified the equation and found the correct solution.

Step-by-step explanation:

In Step 1, Lorena correctly distributed -3 to the parentheses: 5k - 6k + 2 - 9 = 0. Here, she combined like terms by subtracting 6k from 5k, which gave her -k: -k + 2 - 9 = 0. In Step 3, she correctly applied the multiplication property of equality to isolate the variable term. She divided both sides of the equation by -1, so the equation became k - 2 + 9 = 0. Finally, in Step 4, she simplified the equation and found the correct solution: k + 7 = 0, k = -7.