Question

What are the first two steps in solving the following equation?

7(3r - 1) - (r + 5) = -52

a. Combine Like Terms, Subtraction Prop of Equality.
b. Distributive Property, Combine Like Terms.
c. Distributive Property, Addition Prop of Equality.
d. Combine Like Terms, Addition Prop of Equality.

Answer 1

The correct steps are option b: Distributive Property to remove parentheses, and then Combine Like Terms to simplify the equation.

Step-by-step explanation:

The first two steps in solving the equation 7(3r - 1) - (r + 5) = -52 are:

1. Apply the Distributive Property to remove the parentheses.
2. Combine Like Terms on both sides of the equation.

So, the correct option is b. Distributive Property, Combine Like Terms.

To further elaborate, applying the Distributive Property, we multiply 7 by each term inside the parentheses. This gives us:

7 * 3r - 7 * 1 - (r + 5) = -52

Which simplifies to:

21r - 7 - r - 5 = -52

Next, we combine like terms, combining all r terms and constants on one side of the equation:

21r - r - 7 - 5 = -52

Which simplifies to:

20r - 12 = -52

This simplification makes it easier to solve for r in the subsequent steps.