Negative three times a number plus four is no more than the number minus eight.

[latex]-3x+4\leq x-8\\ -4x\leq-12\\ x\geq3 [/latex]

[latex][latex]x-\ number\\\\ -3*x+4 \leq x-8\ \ \ \ \ | add \ 8\\\\ -3x+12 \leq x\ \ \ \ |add\ 3x\\\\ 12 \leq 4x\ \ \ \| divide\ by\ 4\\\\x \geq \frac{12}{4}\\\\x \geq 3[/latex]