Final answer:
To model the equation 9x+2=8x+(-6) with algebra tiles, you would use 9 positive x-tiles and 2 positive unit tiles for the left side, and 8 positive x-tiles and 6 negative unit tiles for the right side. Simplifying, the value of x is -8.
Step-by-step explanation:
The task is to model the equation 9x+2=8x+(-6) using algebra tiles. To model this equation, we will represent the variables and constant terms with tiles, with each 'x-tile' representing a variable 'x', and each unit tile representing the numeral 1 or -1. Let's break down the equation into two sides and model accordingly.
Left Side of the Equation
For the left side, we have 9x+2. This would be represented as:
9 positive x-tiles for the 9x part.
2 positive unit tiles for the +2 part.
Right Side of the Equation
On the right side, we have 8x+(-6). This translates to:
8 positive x-tiles for the 8x part.
6 negative unit tiles for the -6 part.
To find a solution, we would remove 8 x-tiles from both sides to simplify the equation. This would leave us with 1x + 2 = -6. Removing 2 positive unit tiles from the left side, we have 1x = -8. Thus, the value of x is -8.