Question

writing andrew plans to build a tree house that is \\(\frac{1}{2}\\) the size of cynthias tree house. andrew plans to make the area of his tree house at least 14 square feet. write and solve an inequality to find the area of cynthias tree house. use pencil and paper. describe how you know which tree house is larger without solving the inequality.
let x be the area of cynthias tree house. complete the inequality.
\\(\frac{1}{2}x\\) \\(\boldsymbol{\text{blank}}\\) 14

Explanation:

Step1: Analyze the problem

Andrew's tree house area is $\frac{1}{2}x$ (where $x$ is Cynthia's tree house area), and Andrew's tree house area is at least 14 square feet. So the inequality is $\frac{1}{2}x \geq 14$.

Step2: Solve the inequality

To solve $\frac{1}{2}x \geq 14$, multiply both sides by 2: $x \geq 28$.

Step3: Determine which is larger

Since Andrew's tree house area is half of Cynthia's ($\frac{1}{2}x$), and $\frac{1}{2} < 1$, Cynthia's tree house area ($x$) must be larger than Andrew's ($\frac{1}{2}x$) because we're taking a fraction (less than 1) of Cynthia's area to get Andrew's.

Answer:

The inequality is $\frac{1}{2}x \geq 14$, the solution is $x \geq 28$, and Cynthia's tree house is larger because Andrew's area is a fraction (1/2) of Cynthia's, so Cynthia's area must be greater.