Question

problem 3
in the diagram shown, x represents the weight of
each triangle, and 3 represents the weigh of each
square.
select all the equations that could represent a
balanced hanger.
□ 6x = 6
□ x + 9 = 3x + 3
□ 6 = 2x
□ 6 + 12x = 12 + 6x
□ 2x + 12 = 4x + 6

Explanation:

Step1: Calculate the left - hand side weight

There are \(2\) triangles and \(4\) squares on the left. The weight of triangles is \(2x\), and the weight of squares is \(4\times3 = 12\). So the total weight on the left is \(2x + 12\).

Step2: Calculate the right - hand side weight

There are \(4\) triangles and \(2\) squares on the right. The weight of triangles is \(4x\), and the weight of squares is \(2\times3=6\). So the total weight on the right is \(4x + 6\).

Step3: Check each equation

• For \(6x = 6\), it does not match the weight relationship of the hanger.
• For \(x + 9=3x + 3\), it does not match the weight relationship of the hanger.
• For \(6 = 2x\), it does not match the weight relationship of the hanger.
• For \(6 + 12x=12 + 6x\), it does not match the weight relationship of the hanger.
• For \(2x + 12=4x + 6\), it matches the weight relationship of the hanger.

Answer:

\(2x + 12 = 4x + 6\)