Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.

Question

^{x^2-14x+48>0}

Use the inequality in the form

​f(x)>​0,

to write the intervals determined by the boundary points as they appear from left to right on a number line.

interval: ___ ___ ____

sign: + or - + or - + or -

(Type your answers in interval notation. Use ascending​ order.)

The solution set is:

Choose the correct graph below.

A.

An infinite number line, labeled from negative 1 to 10, has tick marks in increments of 1 where every tick is labeled.-1012345678910

B.

An infinite number line, labeled from negative 1 to 10, has tick marks in increments of 1 where every tick is labeled. There is a closed square bracket at 6 and an open square bracket at 8. The portion of the number line to the left of 6 is shaded and the portion to the right of 8 is shaded.-1012345678910

C.

An infinite number line, labeled from negative 1 to 10, has tick marks in increments of 1 where every tick is labeled. The number line is shaded completely.-1012345678910

D.

An infinite number line, labeled from negative 1 to 10, has tick marks in increments of 1 where every tick is labeled. There is an open parenthesis at 6 and a closed parenthesis at 8. The portion of the number line between 6 and 8 is shaded.-1012345678910

E.

An infinite number line, labeled from negative 1 to 10, has tick marks in increments of 1 where every tick is labeled. There is a closed parenthesis at 6 and an open parenthesis at 8. The portion of the number line to the left of 6 is shaded and the portion to the right of 8 is shaded.-1012345678910

F.

An infinite number line, labeled from negative 1 to 10, has tick marks in increments of 1 where every tick is labeled. There is an open square bracket at 6 and a closed square bracket at 8. The portion of the number line between 6 and 8 is shaded.-1012345678910

Answer 1

x² - 14x + 48 > 0

(x - 6)(x - 8) > 0

When x < 6, x - 6 and x - 8 are both negative, so (x - 6)(x - 8) > 0

When 6 < x < 8, x - 6 is positive and x - 8 is negative, so (x - 6)(x - 8) < 0

When x > 8, x - 6 and x - 8 are both positive, so (x - 6)(x - 8) > 0

Solution set (-∞, 6) ∪ (8, ∞)

Answer 2

(x-6)(x-8)>0

either x-6 and x-8 are both >0 or both are <0

x-6>0

x>6

x-8>0

x>8

or

x-6<0

x <6

x-8<0

x<8

either x<6 or x>8

in interval notation (-infinity, 6) U (8, infinity)

graphically,on a real number line put open dots, small circles at 6 and 8

then draw a dark line to the left of 6 and to the right of 8

put an arrow at the end of the leftward line to indicate the line goes forever

same with an arrow at the end of the rightward line

the rest of the questions seem to suggest you are limiting the answer to -1<x<6 and 8<x<10

that would change the answer in interval notation to (-1,6)U(8,10)

or [-1,6)U(8,10] if you include the end points -1 and 10

or maybe you're just limiting the answer to integers between -1 and 10

then the answer is -1,0,1,2,3,4,5 and 9,10 if you include the endpoints

Answer 3