Question

remember to show all your work. you may use the back of the worksheet or a separate piece of paper.

1. riley and cindy are solving the equation \\(7(x + 2) = 91\\). riley starts by using the distributive property. cindy starts by dividing each side by 7.

a. show what rileys and cindys full solution methods might look like.

Explanation:

Write the initial equation

We begin with the given equation:

$$7(x + 2) = 91$$

Show Riley's solution method

Riley starts by applying the Distributive Property to expand the left side:

$$7 \cdot x + 7 \cdot 2 = 91$$

$$7x + 14 = 91$$

Next, solve the Two-Step Equations by subtracting \(14\) from both sides:

$$7x = 77$$

Finally, apply the Division Property of Equality by dividing both sides by \(7\):

$$x = 11$$

Show Cindy's solution method

Cindy starts by using the Division Property of Equality to divide both sides by \(7\):

$$\frac{7(x + 2)}{7} = \frac{91}{7}$$

$$x + 2 = 13$$

Next, solve the remaining equation by subtracting \(2\) from both sides:

$$x = 11$$

Compare the methods

Both methods are mathematically correct and lead to the same final solution:

$$x = 11$$

Answer:

Riley's Method:

$$
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Cindy's Method:

$$
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