Question

To model algebraic expressions, you use squares for x and circles for 1. You shade the shapes to indicate negative. For a given algebraic expression, you draw 2 unshaded squares, 1 shaded square, 2 unshaded circles, and 2 shaded circles. Which algebraic expression is equivalent to the algebraic expression that you modeled? (1 point) Responses 3x+4 3 x plus 4 x x 3x 3 x x+4

Answer 1

To interpret the shapes you've described:

- **Unshaded squares (x)**: Represent positive \( x \), and you have 2 of them, which equals \( 2x \).
- **Shaded squares (-x)**: Represent negative \( x \) (or -1 for each x), and you have 1 shaded square, which equals \(-x\).
- **Unshaded circles (1)**: Represent positive 1, and you have 2 of them, which equals \( 2 \).
- **Shaded circles (-1)**: Represent negative 1 (or -1 for each circle), and you have 2 shaded circles, which equals \(-2\).

Now let's combine these:

1. Combine the contributions from the squares:
\[
2x - x = x
\]

2. Combine the contributions from the circles:
\[
2 - 2 = 0
\]

Putting it all together, the algebraic expression represented by your model is:
\[
x + 0 = x
\]

So, none of the responses provided (3x + 4, 3x, x + 4) exactly matches \( x \). Assuming there is an oversight, if \( x \) was meant to be included in terms of options, the equivalent expression would simply be:
\[
x
\]
However, since this isn't one of the listed responses, it seems like there may be a misunderstanding or error regarding the options provided.