Explore algebraic equivalence with the following investigation.
- Enter the expression 2x into the red pan, and enter the expression x + 4 into the blue pan.
- Enter the value x = -5 into the box near the top. What happens? Change the value of x to 0 and then to 5. How does this change the relationship between the pans?
- Find a value of x such that the red pan equals 0. Where is the red dot when the red pan has a value of 0?
- Find a value of x such that the blue pan equals 0. Where is the blue dot when the blue pan has a value of 0?
- Move the slider to adjust the value of x. For what value of x do the red and blue pans have equal values? What happens in the graph when the values of the pans are equal?
- What other observations can you make about the relationship between the values of the pans and the graph?