Answer
The set- builder notation for all real numbers that satisfy the given condition is\[\left\{ x|x\le 4 \right\}\].
Work Step by Step
Let us suppose the number is \[x\].
Then, the algebraic form of the inequality is:
\[x+12\ge 4x\]
And now to find out possible values of \[x\] satisfying the inequality the inequality is solved as follows:
\[\begin{align}
& x+12\ge 4x \\
& 12\ge 4x-x \\
& 12\ge 3x \\
& 4\ge x
\end{align}\]
Hence all the real numbers less than or equal to 4 will satisfy the condition.
The set-builder form for the inequality obtained is:
\[\left\{ x|x\le 4 \right\}\]
The set- builder notation for all real numbers that satisfy the given condition is\[\left\{ x|x\le 4 \right\}\].
