Đáp án:
1. x≥$\dfrac{1}{3}$
2. x≤$\dfrac{5}{2}$
3.x>2
4. x≥$\dfrac{1}{2}$
5. $\left \{ {{x≤3} \atop {x≥\dfrac{-2}{7}}} \right.$
6. -3≤x<7
7. 0≤x≤2
8. ∀x
9. \(\left[ \begin{array}{l}x≤-\sqrt{2}\\x≥\sqrt{2}\end{array} \right.\)
10.∀x
11.\(\left[ \begin{array}{l}x≥\dfrac{3}{2}\\x≤-1\end{array} \right.\)
12. \(\left[ \begin{array}{l}x≤2\\x≥3\end{array} \right.\)
13. 3<x<5
14. x≥$\dfrac{1}{6}$
Giải thích các bước giải:
1. 3x-1≥0 ⇔ x≥$\dfrac{1}{3}$
2. 5-2x≥0 ⇔ x≤$\dfrac{5}{2}$
3. 7x-14>0 ⇔ x>2
4. 2x-1≥0 ⇔ x≥$\dfrac{1}{2}$
5. $\left \{ {{3-x≥0} \atop {7x+2≥0}} \right.$ ⇔ $\left \{ {{x≤3} \atop {x≥\dfrac{-2}{7}}} \right.$
6. $\left \{ {{\dfrac{x+3}{7-x}≥0} \atop {7-x}\neq0} \right.$
⇔ -3≤x<7
7. 2x-x²≥0 ⇔ 0≤x≤2
8. x²+3≥0 đúng ∀x
9. x²-2≥0 ⇔ \(\left[ \begin{array}{l}x≤-\sqrt{2}\\x≥\sqrt{2}\end{array} \right.\)
10. x²-3x+7≥0 đúng ∀x
11. 2x²-5x+3≥0 ⇔ \(\left[ \begin{array}{l}x≥\dfrac{3}{2}\\x≤-1\end{array} \right.\)
12. x²-5x+6≥0 ⇔ \(\left[ \begin{array}{l}x≤2\\x≥3\end{array} \right.\)
13. $\left \{ {{x-3>0} \atop {5-x>0}} \right.$ ⇔ 3<x<5
14. $\left \{ {{6x-1≥0} \atop {x+3≥0}} \right.$ ⇔ $\left \{ {{x≥3} \atop {x≥\dfrac{1}{6}}} \right.$
⇔ x≥$\dfrac{1}{6}$
