Question

geometry identify an inequality that represents x (in centimeters).
area ≥ 120 cm²
10 cm
10 + 10 + x + x ≥ 120
10x ≥ 120
10·10·x·x ≥ 120
10x ≤ 120
solve the inequality.
the solution is

Explanation:

Step1: Recall the area formula for a rectangle

The area formula for a rectangle is \(A = length\times width\). Here, the width is \(10\) cm and the length is \(x\) cm, so \(A = 10x\).

Step2: Set up the inequality based on the area condition

Since \(Area\geq120\mathrm{cm}^2\), substituting the area formula gives \(10x\geq120\).

Step3: Solve the inequality \(10x\geq120\)

Divide both sides of the inequality by \(10\). Using the property of inequalities \(\frac{10x}{10}\geq\frac{120}{10}\), which simplifies to \(x\geq12\).

Answer:

The correct inequality is \(10x\geq120\). The solution is \(x\geq12\).