Question

samuel is solving the equation $3(x - 1) + 4 = 2 - (x + 3)$. which equivalent equations might samuel use? check all that apply.\
$\square\\ 3x - 3 + 4 = 2 - x - 3$\
$\square\\ 3x - 1 + 4 = 2 - x + 3$\
$\square\\ 3x - 3 + 4 = 2 - x + 3$\
$\square\\ 3x + 1 = -x - 1$\
$\square\\ 3x + 3 = -x + 5$\
$\square\\ 3x + 1 = -x + 5$

Explanation:

Step1: Apply Distributive Property

For the left side \(3(x - 1)+4\), distribute 3: \(3x-3 + 4\).
For the right side \(2-(x + 3)\), distribute the negative sign: \(2 - x-3\).
So the equation becomes \(3x-3 + 4=2 - x-3\) (first option is valid).

Step2: Simplify Both Sides

Simplify left side: \(3x-3 + 4=3x + 1\).
Simplify right side: \(2 - x-3=-x - 1\).
So the equation becomes \(3x + 1=-x - 1\) (fourth option is valid).

Step3: Check Other Options

• Second option: \(3(x - 1)\) distributed incorrectly (should be \(3x-3\), not \(3x - 1\)), so invalid.
• Third option: Right side distribution incorrect (should be \(-x - 3\), not \(-x + 3\)), invalid.
• Fifth option: Left and right simplification wrong, invalid.
• Sixth option: Right side simplification wrong (should be \(-x - 1\), not \(-x + 5\)), invalid.

Answer:

A. \(3x - 3 + 4 = 2 - x - 3\), D. \(3x + 1 = -x - 1\)