Question

1. write and solve an inequality that represents the values of x for which the area of the rectangle will be at least 35 square feet.

Explanation:

Step1: Write the area formula

The area \(A\) of a rectangle is \(A = \text{length}\times\text{width}\). Here, length \(l=(x - 2)\) ft and width \(w = 5\) ft. So, \(A=5(x - 2)\).
Since the area is at least \(35\) square feet, the inequality is \(5(x - 2)\geq35\).

Step2: Solve the inequality

Divide both sides of the inequality \(5(x - 2)\geq35\) by \(5\):
\(\frac{5(x - 2)}{5}\geq\frac{35}{5}\), which simplifies to \(x-2\geq7\).
Add \(2\) to both sides: \(x-2 + 2\geq7+2\).

Answer:

The inequality is \(5(x - 2)\geq35\). The solution is \(x\geq9\).