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 inequality for the area

The area \(A\) of a rectangle is given by \(A=\text{length}\times\text{width}\). Here, length \( = 5\) ft and width \(=x - 2\) ft. We want the area to be at least \(35\) square feet. So the inequality is \(5(x - 2)\geq35\).

Step2: Distribute the 5

Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 5\), \(b=x\), \(c=- 2\)), we get \(5x-10\geq35\).

Step3: Add 10 to both sides

To isolate the term with \(x\), add \(10\) to both sides of the inequality. \(5x-10 + 10\geq35+10\), which simplifies to \(5x\geq45\).

Step4: Divide both sides by 5

Divide each side of the inequality \(5x\geq45\) by \(5\). \(\frac{5x}{5}\geq\frac{45}{5}\), so \(x\geq9\).

Answer:

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