Hanger Diagrams: Solving Equations
This worksheet helps students understand and solve algebraic equations using the visual model of hanger diagrams.
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Hanger Diagrams: Solving Equations
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Use the concept of hanger diagrams (balance scales) to solve each equation. Remember, to keep the hanger balanced, whatever you do to one side, you must do to the other side.
1. If a hanger is balanced with 3 circles on the left side and 6 squares on the right side, and all circles have the same weight ('x') and all squares have the same weight (1 unit), what equation does this represent?
2. Draw a hanger diagram that represents the equation x + 2 = 5.
For each hanger diagram, write an equation and solve for 'x'.
Equation:
Equation:
3. The equation 2x + 1 = 7 can be represented by a hanger with two 'x' weights and one '1' weight on one side, balanced with '1' weights on the other side.
4. To solve 3x = 9 using a hanger diagram, you would divide the weights on both sides into equal groups.
5. Which operation would you perform first to solve the equation 4x + 5 = 17 using a hanger diagram?
Add 5 to both sides
Subtract 5 from both sides
Multiply both sides by 4
Divide both sides by 4
6. Imagine a hanger diagram where one side has 2 'x' weights and 4 '1' weights, and the other side has an 'x' weight and 7 '1' weights. Write the equation this represents and solve for 'x'.