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: $$+2x-x=+1x(\text{which is simply }x)$$

• 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: $$\boxed{{\displaystyle x}}$$