Respuesta :
Answer:
The inequality for [tex]x[/tex] is:
[tex]x\geq 142[/tex]
Step-by-step explanation:
Given:
Width of rectangle = 3 ft
Height or length of rectangle = [tex](x+5)[/tex] ft
Perimeter is at least 300 ft
To write an inequality for [tex]x[/tex].
Solution:
Perimeter of a rectangle is given as:
⇒ [tex]2l+2w[/tex]
where [tex]l[/tex] represents length of the rectangle and [tex]w[/tex] represents the width of the rectangle.
Plugging in the given values in the formula, the perimeter can be given as:
⇒ [tex]2(x+5)+2(3)[/tex]
Using distribution:
⇒ [tex]2x+10+6[/tex]
Simplifying.
⇒ [tex]2x+16[/tex]
The perimeter is at lest 300 ft. So, the inequality can be given as:
⇒ [tex]2x+16\geq 300[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 16.
⇒ [tex]2x+16-16\geq 300-16[/tex]
⇒ [tex]2x\geq284[/tex]
Dividing both sides by 2.
⇒ [tex]\frac{2x}{2}\geq \frac{284}{2}[/tex]
⇒ [tex]x\geq 142[/tex] (Answer)
