Question

carmen solves this equation $11x - 7 = 7(x + 2) - 3x$. the steps she uses to solve the equation are shown. select an answer choice from each drop-down list to describe each step
$11x - 7 = 7(x + 2) - 3x$
$11x - 7 = 7x + 14 - 3x$
$11x - 7 = 7x - 3x + 14$
$11x - 7 = 4x + 14$
$7x - 7 = 14$
$7x = 21$
$x = 3$

Explanation:

Step1: Apply Distributive Property

$11x - 7 = 7(x+2) - 3x \implies 11x - 7 = 7x + 14 - 3x$

Step2: Rearrange Like Terms

$11x - 7 = 7x + 14 - 3x \implies 11x - 7 = 7x - 3x + 14$

Step3: Combine Like Terms

$11x - 7 = 7x - 3x + 14 \implies 11x - 7 = 4x + 14$

Step4: Subtract $4x$ from Both Sides

$11x - 7 - 4x = 4x + 14 - 4x \implies 7x - 7 = 14$

Step5: Add 7 to Both Sides

$7x - 7 + 7 = 14 + 7 \implies 7x = 21$

Step6: Divide by 7 on Both Sides

$\frac{7x}{7} = \frac{21}{7} \implies x = 3$

Answer:

$x=3$
---
Corresponding step descriptions (to match the dropdowns):

1. Distribute $7$ to $(x+2)$
2. Rearrange the $x$-terms
3. Combine $7x-3x$ to $4x$
4. Subtract $4x$ from each side
5. Add $7$ to each side
6. Divide each side by $7$