Nosaira solved an equation. her work is shown below: 3(2x + 1 ) = 2(x + 1) + 1 6x + 3 = 2x + 2 + 1 6x + 3 = 2x + 3 4x = 0 x = 0 she determines the equation has no solution. which best describes nosaira’s work and answer? her work is correct, but there is one solution rather than no solution. her work is correct and her interpretation of the answer is correct. her work is incorrect. she distributed incorrectly. her work is incorrect. she moved terms across the equals sign incorrectly.

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.