Which is the correct way to model the equation Negative x + 8 = 7 x + (negative 8) using algebra tiles?

Question

1 positive x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 positive unit tiles on the right side
8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
8 positive x-tiles and 1 negative unit tile on the left side; 8 negative x-tiles and 7 positive unit tiles on the right side

Answer 1

To model the equation \(-x + 8 = 7x + (-8)\) using algebra tiles, let's break it down:

1. The left side of the equation is \(-x + 8\):

   • This means you have 1 negative \(x\)-tile and 8 positive unit tiles.

2. The right side of the equation is \(7x + (-8)\):

   • This translates to 7 positive \(x\)-tiles and 8 negative unit tiles.

Thus, the correct way to model the equation using algebra tiles is:

1 negative \(x\)-tile and 8 positive unit tiles on the left side; 7 positive \(x\)-tiles and 8 negative unit tiles on the right side.

This corresponds to the option:

3. 1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side.