Is 6x-4=-4+6x true for all one or no values

There are infinite solutions

Step-by-step explanation:

6x-4=-4+6x

Subtract 6x from each side

6x-6x-4=-4+6x-6x

-4 = -4

This is always true, so no matter what value of x  you put in, the equation is true.

There are infinite solutions

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.