Absolutely, let's go through each step in the solution to identify the properties of equality applied in steps 2 and 4.
1. The equation starts as:
[tex]\[-7n + 11 = -10\][/tex]
2. In step 2, you see:
[tex]\[-7n + 11 - 11 = -10 - 11\][/tex]
Here, the same number (11) is subtracted from both sides of the equation. This is using the additive property of equality. The additive property states that if you add or subtract the same amount from both sides of an equation, the equality is maintained.
3. In step 3, it simplifies to:
[tex]\[-7n = -21\][/tex]
4. In step 4, you have:
[tex]\[\frac{-7n}{-7} = \frac{-21}{-7}\][/tex]
Here, both sides of the equation are divided by the same number (-7). This employs the division property of equality. The division property asserts that dividing both sides of an equation by the same nonzero number keeps the equation balanced.
5. In step 5, the equation simplifies to:
[tex]\[n = 3\][/tex]
So, based on the steps and the solutions shown:
- In step 2: the additive property of equality was applied.
- In step 4: the division property of equality was applied.
