Sure! Let's analyze the steps in the solution of the given equation to identify the mathematical properties applied at each stage:
1. Initial Equation:
[tex]\[
-7n + 11 = -10
\][/tex]
2. Step 2:
[tex]\[
-7n + 11 - 11 = -10 - 11
\][/tex]
Here, both sides of the equation have 11 subtracted. This is the subtraction property of equality, which allows us to subtract the same number from both sides of the equation without changing the equality.
3. Step 3:
[tex]\[
-7n = -21
\][/tex]
After subtracting 11 from both sides, we simplify to reach this step.
4. Step 4:
[tex]\[
\frac{-7n}{-7} = \frac{-21}{-7}
\][/tex]
Here, both sides of the equation are divided by -7. This is the division property of equality, which allows us to divide both sides of an equation by the same non-zero number.
5. Step 5:
[tex]\[
n = 3
\][/tex]
After dividing both sides by -7, we simplify to reach the final solution.
So, the completed statements should be:
- In step 2, the subtraction property of equality was applied.
- In step 4, the division property of equality was applied.
