Need some madwill mark the brainiest

1. simplify 5(a - b) + 6(a + b) - 7(a - 2b)
4a - 13b
4a + 15b
19ab

2. simplify 5(x - 2) + 6
5x + 4
5x - 4
5x + 20

3. simplify 6(x - 3) - 4(x + 1)
2x - 22
2x - 14
2x - 2

4. simplify 7(x - 1) - 2(x + 1) + 3(x - 4)
8x - 21
8x - 4
8x + 21

5.10(x + 4) + 15(x + 1)
25x + 55
25x + 5
55x

6. simplify 7(9x - 3) - 4(2x - 1)
34x
55x - 17
55x - 25

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.