Question

2 explain how the parts of the balanced hanger compare to the parts of the equation. 7 = 2x + 3

Explanation:

Step1: Analyze the hanger's left side

The left side of the hanger has 7 square - shaped weights. In the equation \(7 = 2x+3\), the left - hand side of the equation is 7. So the 7 squares on the left side of the hanger correspond to the left - hand side of the equation, which is 7.

Step2: Analyze the hanger's right side

The right side of the hanger has 2 circular weights (let's say each circle represents \(x\)) and 3 square weights. In the equation \(7 = 2x + 3\), the right - hand side is \(2x+3\). The 2 circular weights represent the \(2x\) term (since each circle can be thought of as a variable \(x\)) and the 3 square weights represent the constant term 3. The balance of the hanger (left side weight = right side weight) is analogous to the equality in the equation \(7=2x + 3\), where the total weight on the left (7) is equal to the total weight on the right (\(2x + 3\)).

Answer:

On the balanced hanger, the left - hand side with 7 square weights corresponds to the left - hand side of the equation \(7 = 2x+3\) (the value 7). The right - hand side of the hanger, which has 2 circular weights (representing \(2x\), as each circle is a variable \(x\)) and 3 square weights (representing the constant 3), corresponds to the right - hand side of the equation \(2x + 3\). The balance of the hanger (left weight = right weight) is like the equality in the equation (left - hand side value = right - hand side value).