Solve the following equations
a) 2(x - 1) = 4 (x + 2)
b)(3 - x) (x + 2) = 0

see below

Step-by-step explanation:

a) 2(x - 1) = 4 (x + 2)

Distribute

2x-2 = 4x+8

Subtract 2x from each side

2x-2x-2 = 4x-2x +8

-2 = 2x+8

Subtract 8 from each side

-2-8 = 2x+8-8

-10=2x

Divide each side by 2

-10/2 = 2x/2

-5 =x

b)(3 - x) (x + 2) = 0

We can use the zero product property

3-x = 0    x+2= 0

3-x+x=0+x     x+2-2=0-2

3=x                x=-2

did you get the answer yet?

step-by-step explanation:

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.