Example of solving an equation in algebra using properties of equality.

Let's solve the equation in the "Now You Try" section step by step, using the Properties of Equality, and provide a justification for each step.

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Equation to Solve:

$$
4m - 8 = -12
$$

We will fill out the table with steps and justifications.

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Step-by-Step Solution:

| Step | Justification |
|-----------------------------|--------------------------------------------|
| $ 4m - 8 = -12 $ | Given |
| $ 4m - 8 + 8 = -12 + 8 $ | Addition Property of Equality |
| $ 4m = -4 $ | Simplify |
| $ \frac{4m}{4} = \frac{-4}{4} $ | Division Property of Equality |
| $ m = -1 $ | Simplify |

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✔ Explanation of Each Step:

1. Given:
The original equation is provided.

2. Addition Property of Equality:
We add 8 to both sides to eliminate the constant term on the left side. This maintains the equality because we are doing the same thing to both sides.

3. Simplify:
$-8 + 8 = 0$, so the left side becomes $4m$. On the right side, $-12 + 8 = -4$.

4. Division Property of Equality:
We divide both sides by 4 to isolate $m$. Since both sides are divided by the same nonzero number, the equality holds.

5. Simplify:
$ \frac{4m}{4} = m $, and $ \frac{-4}{4} = -1 $, so $ m = -1 $.

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✔ Final Answer:

$$
\boxed{m = -1}
$$

This solution satisfies the original equation:
$$
4(-1) - 8 = -4 - 8 = -12 \quad \text{✓}
$$

Let me know if you'd like this formatted as a table or printed version!