Answer:
[tex]5(x + 7)(x + 7) \geq 1050[/tex]
Yes, 8 inches is a reasonable width for the tablet.
Step-by-step explanation:
Let x be the width of the tablet.
If the width of the television screen is 7 inches more than the width of the tablet, then:
[tex]\textsf{Width of television screen} = x + 7[/tex]
Given that the length of the television screen is 5 times its width, then:
[tex]\textsf{Length of television screen} = 5(x + 7)[/tex]
At the television screen can be modelled as a rectangle, its area is the product of its length and width:
[tex]\textsf{Area of television screen} = 5(x + 7)(x + 7)[/tex]
Given that the area of the new television screen should be at least 1,050 square inches then we can set the expression for the area of the television screen to more than or equal to 1050:
[tex]5(x + 7)(x + 7) \geq 1050[/tex]
To determine if 8 inches is a reasonable width for the tablet, we need to check whether it satisfies the inequality by substituting x = 8 into the inequality:
[tex]\[ 5(8 + 7)(8 + 7) \geq 1050\\\\5(15)(15) \geq 1050\\\\5(225) \geq 1050 \\\\1125 \geq 1050 \][/tex]
Since 1125 is greater than or equal to 1050, the inequality holds true when x = 8.
Therefore, 8 inches is a reasonable width for the tablet because it satisfies the condition that the area of the new television screen is at least 1,050 square inches.
