To model algebraic expressions, you use squares for x and circles for 1. You shade the shapes to indicate negative.

Question

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

3x
3 x

x+4
x plus 4

x

Answer 1

To interpret the shapes you've drawn:

• Each square represents \( x \), so you have:
  • 2 unshaded squares (positive \( x \)): \( +2x \)
  • 1 shaded square (negative \( x \)): \( -x \)

Combining these gives: \[ +2x - x = +1x \quad (\text{which is simply } x) \]

• Each circle represents \( 1 \), so you have:
  • 2 unshaded circles (positive \( 1 \)): \( +2 \)
  • 2 shaded circles (negative \( 1 \)): \( -2 \)

Combining these gives: \[ +2 - 2 = 0 \]

Putting it all together, the overall expression is: \[ x + 0 = x \]

Therefore, the algebraic expression that is equivalent to the expression you modeled is: \[ \boxed{x} \]