Answer
\[\left\{ x\le 50 \right\}\].
Work Step by Step
Let us suppose the number is \[x\].
Then, the algebraic form of the inequality is:
\[\frac{3x}{5}\,+4\,\le 34\]
And now to find out possible values of \[x\] satisfying the inequality the inequality is solved as follows:
\[\begin{align}
& \frac{3x}{5}\,+4\,\le 34 \\
& \frac{3x\times 5}{5}\,+4\times 5\,\le 34\times 5 \\
& 3x\,+20\le 170
\end{align}\]
This can be further simplified as:
\[\begin{align}
& 3x\le 150 \\
& \frac{3x}{3}\le \frac{150}{3} \\
& x\le \text{ }50
\end{align}\]
Hence all the real numbers less than or equal to 50 will satisfy the condition.
The set-builder form of the inequality obtained is:
\[\left\{ x\,x\le \,50 \right\}\]
Therefore, the number can be represented in set builder form as \[\left\{ x\le 50 \right\}\].
