Answer
\[\left\{ x\ge 16 \right\}\].
Work Step by Step
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 \[\left\{ x\ge 16 \right\}\].
