Question about relationship between two inequality equations

Question

Known: $$X_1=A_1+B_1$$ $$X_2=A_2+B_2$$ $$X_2=A_2+B_2$$ $$B_1\le B_2 $$

$$B_2\le K*B_1 $$ $$ K\ge1$$ $$ X_1\le X_2$$ Is it true that: $$X_2\le K*X_1 $$ If not true, are there conditions that make it true?

Answer 1

Hint:   not true in general, but sufficient conditions could be $\,A_2 \le K \cdot A_1\,$ or $\,A_2 \le A_1\,$, since:

$$ X_2 =A_2 + B_2 \le A_2+ K \cdot B_1 = A_2+K \cdot(X_1-A_1) = K \cdot X_1+ A_2 - K \cdot A_1 $$