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The distributive property is a fundamental concept in algebra that allows us to multiply a number by a sum or difference within parentheses. For instance, the problem dealing with the equation
$$7(b-3) = 10b$$
calls for the use of the distributive property in the first step. It involves multiplying the number 7 (outside the parentheses) with each term inside the parentheses (b and -3). In essence, you're distributing the 7 like this:
$$7 \cdot b - 7 \cdot 3$$
This step is crucial because it transforms the equation into a simpler form, specifically
$$7b - 21 = 10b$$
Generally, when utilizing the distributive property, remember to multiply each term inside the parentheses by the exterior number. This essential process prepares the equation for further simplification and ultimately, solving.

Rearranging equations is a strategic step towards isolating the variable you're solving for. It involves moving terms from one side of the equation to the other usually by adding, subtracting, multiplying, or dividing both sides by the same number. In our example, after applying the distributive property, the equation becomes
$$7b - 21 = 10b$$
To rearrange, we want to group like terms and constants on different sides. Subtracting 7b from both sides gives us
$$-21 = 10b - 7b$$
which simplifies to
$$-21 = 3b$$
The variable, b, is now on one side of the equation, and the constant is on the other, neatly setting up the equation for the final step of solving for b. Remember, the goal of rearranging is to simplify and clear the path towards finding the value of the unknown variable.

Once a solution to an equation is found, it's important to verify its accuracy. Checking the solution involves substituting the variable back into the original equation to see if the equation remains true. In our problem, after solving, we have found that
$$b = -7$$
To check the solution, we substitute -7 back into the original equation to get:
$$7(-7 - 3) = 10 \cdot -7$$
Upon simplifying, we end up with:
$$-70 = -70$$
Since both sides of the equation are equal, our solution is confirmed to be correct. Always remember to check your solutions to ensure they satisfy the original equation. This verifying step is what ultimately validates your algebraic efforts.