Question

1. write and solve the equation modeled below:

equation:
image of a balance scale with 4 x - tiles and 4 -1 tiles on the left, and 4 -x tiles and 2 -1 tiles on the right
solution:

Explanation:

Step1: Analyze the balance model

Left side: 4 \( x \) tiles and 4 \( -1 \) tiles, so expression is \( 4x + 4(-1) \) or \( 4x - 4 \).
Right side: 4 \( -x \) tiles and 2 \( -1 \) tiles, so expression is \( 4(-x) + 2(-1) \) or \( -4x - 2 \).
Since the balance is equal, the equation is \( 4x - 4 = -4x - 2 \).

Step2: Solve the equation

Add \( 4x \) to both sides:
\( 4x + 4x - 4 = -4x + 4x - 2 \)
\( 8x - 4 = -2 \)

Add 4 to both sides:
\( 8x - 4 + 4 = -2 + 4 \)
\( 8x = 2 \)

Divide both sides by 8:
\( x = \frac{2}{8} = \frac{1}{4} \)

Answer:

Equation: \( 4x - 4 = -4x - 2 \)
Solution: \( x = \frac{1}{4} \)