## Thinking Mathematically (6th Edition)

$\left\{ x\ge 16 \right\}$.
Let us suppose the number is $x$. Then, the algebraic form of the inequality is: $\frac{3x}{4}\,-3\,\ge 9$ And now to find out possible values of $x$ satisfying the inequality the inequality is solved as follows: \begin{align} & \frac{3x}{4}\,-3\,\ge 9 \\ & \frac{3x\times 4}{4}\,-3\times 4\,\ge 9\times 4 \\ & 3x\,-12\ge 36 \end{align} This can be further simplified as: \begin{align} & 3x-12+12\ge 36+12 \\ & 3x\ge 48 \\ & \frac{3x}{3}\ge \frac{48}{3} \\ & x\ge \text{ }16 \end{align} Hence all the real numbers greater than or equal to 16 will satisfy the condition. The set-builder form of the inequality obtained is: $\left\{ x\ge 16 \right\}$ Therefore, the number can be represented in set builder form as $\left\{ x\ge 16 \right\}$.