## Thinking Mathematically (6th Edition)

The set- builder notation for all real numbers that satisfy the given condition is$\left\{ x|x\le 4 \right\}$.
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$\left\{ x|x\le 4 \right\}$.