To represent algebraic equations, you use squares for x and circle for 1. You shade the shapes to represent negative values. You draw a vertical line to represent the equal sign.

Question

How could you represent 3x−1=5
using the shapes?

(1 point)
Responses

Place 3 shaded squares and 1 unshaded circle to the left of the line, and place 5 shaded circles to the right of the line.
Place 3 shaded squares and 1 unshaded circle to the left of the line, and place 5 shaded circles to the right of the line.

Place 3 shaded circles and 1 unshaded square to the left of the line, and place 5 shaded squares to the right of the line.
Place 3 shaded circles and 1 unshaded square to the left of the line, and place 5 shaded squares to the right of the line.

Place 3 unshaded squares and 1 shaded circle to the left of the line, and place 5 unshaded circles to the right of the line.
Place 3 unshaded squares and 1 shaded circle to the left of the line, and place 5 unshaded circles to the right of the line.

Place 3 unshaded circles and 1 shaded square to the left of the line, and place 5 unshaded squares to the right of the line.

Answer 1

To represent the equation \(3x - 1 = 5\) using the specified shapes, we need to break down the equation:

• \(3x\) represents three squares (for \(x\)).
• \(-1\) represents one shaded circle (since it's negative).
• The \(=\) sign is represented by a vertical line.
• The \(5\) on the right side represents five unshaded circles.

Given this understanding, we can visualize the equation as follows:

On the left side of the vertical line:

• We have 3 unshaded squares (for \(3x\)) and 1 shaded circle (for \(-1\)), which gives us the representation for \(3x - 1\).

On the right side of the vertical line:

• We have 5 unshaded circles (for the number \(5\)).

Thus, the correct representation is:

Place 3 unshaded squares and 1 shaded circle to the left of the line, and place 5 unshaded circles to the right of the line.