Solve the inequality x > 2 - |2x-1|

Step-by-step explanation:

It can be solved analytically or graphically. Graphically is the fastest way if you know how to handle the two lines. Let's rearrange terms in either case:

Graphic: Red line is , solid blue line is , the thin extension is the parent line without the absolute value.

Solving the equation is equivalent to answer "when is the blue line higher than the red one?" Which obviously happens outside the two intercept points. Let's find the first coordinate of both - we don't really care what's the y coordinate of either point.

For the left point, the x coordinate is given by

For the right point, we have

Analytical:

We split the problem in two parts: while the content absolute value is non negative, we have

Which admits as solutions all valeus of x greater than 1 (since both have to be satisfied at once, and values between 1/2 and 1 will not work for the second.

OR, with a negative quantity inside the absolute value, we get

which again is satisfied by all values of x less than -1.

Thus the solution is given by

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3