Andrew wants to purchase a new television with a screen length that is five times its width. the width of the television screen is 7 inches more than the width of his tablet. andrew also wants the area of the new television screen to be at least 1,050 square inches. if x is the width of andrew's tablet, determine which inequality could represent this situation. then, determine if 8 inches is a reasonable width for his tablet.

Part 1) The inequality that represent this situation is  or  

Part 2) Yes, 8 inches is a reasonable width for his tablet

Step-by-step explanation:

Part 1)

Let

L -----> the length of the screen television

W ----> the width of the screen television

x ---->  the width of Andrew's tablet

we know that

------> equation A

----> equation B

The area of the television is

-----> equation C

Substitute equation A and equation B in equation C

------> inequality that represent this situation

Part 2) Determine if 8 inches is a reasonable width for his tablet

For x=8 in

Substitute in the inequality

-----> is true

therefore

Yes, 8 inches is a reasonable width for his tablet

The correct answers are:

5x²+70x+245 ≥ 1050; and

Yes.

Explanation:

Let x be the width of the tablet. Since the width of the TV is 7 inches more than the tablet, the width of the TV would be x+7.

The length of the TV is 5 times the width; this makes the length 5(x+7) = 5x+35.

The area of the TV would be given by

(x+7)(5x+35).

Since Andrew wants the area to be at least 1050, we set the expression greater than or equal to 1050:

(x+7)(5x+35) ≥ 1050

Multiplying this, we have:

x*5x+x*35+7*5x+7*35 ≥ 1050

5x²+35x+35x+245 ≥ 1050

Combining like terms,

5x²+70x+245 ≥ 1050

To see if 8 is a reasonable width for the tablet, we substitute 8 for x:

5(8²)+70(8)+245 ≥ 1050

5(64)+560+245 ≥ 1050

320+560+245 ≥ 1050

1125 ≥ 1050

Since this inequality is true, 8 is a reasonable width.