Each student wrote a two-step equation. Peter wrote the equation 5x – 3 = 14, and Andres wrote the equation 20x - 12 = 56. The teacher looked at their equations and asked them to compare them.
Complete the description of one way in which the equations are similar.

To get Andres' equation, you can multiply every number in Peter's equation by.

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1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.