Which pair of expressions are equivalent?

6 t + 5 + 2 t and 11 t + 5

p + 3 + 2 p and 5 t + 3

3 n + 7 and 4 n + 7

2 x + 2 + 7 x and 9 x + 7

if x = 1, then the answer is 3.5

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.