Question

5 lin and noah are solving the equation $7(x + 2) = 91$.
lin starts by using the distributive property. noah starts by dividing each side by 7.
a. show what lins and noahs full solution methods might look like.

b. what is the same and what is different about their methods?

Explanation:

Lin's Solution:

Step1: Apply distributive property

$7(x+2)=7x+14=91$

Step2: Subtract 14 from both sides

$7x+14-14=91-14$
$7x=77$

Step3: Divide by 7 on both sides

$\frac{7x}{7}=\frac{77}{7}$
$x=11$

Noah's Solution:

Step1: Divide both sides by 7

$\frac{7(x+2)}{7}=\frac{91}{7}$
$x+2=13$

Step2: Subtract 2 from both sides

$x+2-2=13-2$
$x=11$

(Part b):

• Same: Both methods isolate $x$ to solve the equation, use inverse operations (subtraction, division), and result in the same correct answer $x=11$.
• Different: Lin first expands the equation with the distributive property, while Noah first simplifies the equation by dividing both sides by the coefficient outside the parentheses, reversing the order of initial steps.

Answer:

(Part a):
Lin's method:

1. $7(x+2)=7x+14=91$
2. $7x=91-14=77$
3. $x=\frac{77}{7}=11$

Noah's method:

1. $\frac{7(x+2)}{7}=\frac{91}{7} \implies x+2=13$
2. $x=13-2=11$

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