Question

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

5k – 6k + 2 – 9 = 0
–k – 7 = 0
–k = 7
k =
Analyze Lorena’s work to determine which statements are correct. Check all that apply.

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.

Answer 1

Correct statements: Step 1 and Step 4.

- Step 1: True — the distribution giving 5k – 6k + 2 – 9 is correct.
- Step 2: False — she combined 5k and −6k (not 5k and 2k).
- Step 3: False — going from −k − 7 = 0 to −k = 7 used the addition property (adding 7), not the multiplication property.
- Step 4: True — you can multiply both sides of −k = 7 by −1 (or divide by −1) to get k = −7.
- Lorena found the correct solution: False — she stopped at −k = 7 and did not write the final k = −7.