About Lesson
14.7 Irrational Inequalities 无理不等式
Solve the inequalities
解下列不等式
(1) ![Rendered by QuickLaTeX.com \sqrt{3x+2}-3 < 0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c24f20fd44a864535aa19ceac402b915_l3.png)
![Rendered by QuickLaTeX.com \sqrt{3x+2}-3 < 0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c24f20fd44a864535aa19ceac402b915_l3.png)
Answer:
![Rendered by QuickLaTeX.com -\frac{2}{3} \leq x < \frac{7}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3af09b5c1222aa0d35a36ddb46e6c108_l3.png)
(2) ![Rendered by QuickLaTeX.com 1-\sqrt{3-x} < 0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-d3a93a391593627cd30d8aa86f59c598_l3.png)
![Rendered by QuickLaTeX.com 1-\sqrt{3-x} < 0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-d3a93a391593627cd30d8aa86f59c598_l3.png)
Answer:
![Rendered by QuickLaTeX.com x < 2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-d99c93d2e558cbbb18bf3dd72278aec0_l3.png)
(3) ![Rendered by QuickLaTeX.com 2+\sqrt{1-3x}\le0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-b031e1f563b46b58dcbdb396c832d169_l3.png)
![Rendered by QuickLaTeX.com 2+\sqrt{1-3x}\le0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-b031e1f563b46b58dcbdb396c832d169_l3.png)
Answer:
无解
(4) ![Rendered by QuickLaTeX.com \sqrt{2x+3}+2>0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ba5d958779763394cd31ae5f3444e2ea_l3.png)
![Rendered by QuickLaTeX.com \sqrt{2x+3}+2>0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ba5d958779763394cd31ae5f3444e2ea_l3.png)
Answer:
![Rendered by QuickLaTeX.com x \geq -\frac{3}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-94e584f646e859a88141cded1baa52e2_l3.png)
(5) ![Rendered by QuickLaTeX.com \sqrt{x^2+2x}-\sqrt{4-x}>0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-03ad6e07a14ea2be74cb94b1ee299daa_l3.png)
![Rendered by QuickLaTeX.com \sqrt{x^2+2x}-\sqrt{4-x}>0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-03ad6e07a14ea2be74cb94b1ee299daa_l3.png)
Answer:
![Rendered by QuickLaTeX.com x < -4](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3fd722aefb590ddf15e92064ac6d8646_l3.png)
![Rendered by QuickLaTeX.com 1< x \leq 4](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-8880fc1815d2a2a42b6f0f8133c84a29_l3.png)
(6) ![Rendered by QuickLaTeX.com \sqrt{9-x}-\sqrt{2x-1}\geq0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3eaa90d7880b6cf912997f3927c851fe_l3.png)
![Rendered by QuickLaTeX.com \sqrt{9-x}-\sqrt{2x-1}\geq0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3eaa90d7880b6cf912997f3927c851fe_l3.png)
Answer:
![Rendered by QuickLaTeX.com \frac{1}{2} \leq x \leq 3\frac{1}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e1afe465e5eba3f082f335fdba6e9664_l3.png)
(7) ![Rendered by QuickLaTeX.com \sqrt{2-x}<x+4](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1034abfba8935e53a1f873db5a96f8b3_l3.png)
![Rendered by QuickLaTeX.com \sqrt{2-x}<x+4](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1034abfba8935e53a1f873db5a96f8b3_l3.png)
Answer:
![Rendered by QuickLaTeX.com -2 < x \leq 2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-a8d226e5d8d8565528f45d4bfa6ca8ec_l3.png)
(8) ![Rendered by QuickLaTeX.com \sqrt{x+1}\le x-1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e0dac792f2ee3e8c1dbc908f459786e2_l3.png)
![Rendered by QuickLaTeX.com \sqrt{x+1}\le x-1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e0dac792f2ee3e8c1dbc908f459786e2_l3.png)
Answer:
![Rendered by QuickLaTeX.com x \geq 3](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f0cc05b3a3b52113651d1d3faf2af6f4_l3.png)
(9) ![Rendered by QuickLaTeX.com \sqrt{5-x}>x-3](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e19466ff69b6d231d6db64fb3fc7ef35_l3.png)
![Rendered by QuickLaTeX.com \sqrt{5-x}>x-3](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e19466ff69b6d231d6db64fb3fc7ef35_l3.png)
Answer:
![Rendered by QuickLaTeX.com x < 4](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-2f270112f352301dd6ab935d7fbba417_l3.png)
(10) ![Rendered by QuickLaTeX.com \sqrt{x^2-4}>x-1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-871161baf529bb2edcbfde50f55c1040_l3.png)
![Rendered by QuickLaTeX.com \sqrt{x^2-4}>x-1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-871161baf529bb2edcbfde50f55c1040_l3.png)
Answer:
![Rendered by QuickLaTeX.com x \leq -2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-37627cb8f4478498c256dfbe06809ebb_l3.png)
![Rendered by QuickLaTeX.com x > 2\frac{1}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1d38c152043b6add5500c8ec36281790_l3.png)
(11) ![Rendered by QuickLaTeX.com \sqrt{x+1}-\sqrt x>\sqrt{x-1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3243e475acfe475ccf243a5b2e050316_l3.png)
![Rendered by QuickLaTeX.com \sqrt{x+1}-\sqrt x>\sqrt{x-1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3243e475acfe475ccf243a5b2e050316_l3.png)
Answer:
![Rendered by QuickLaTeX.com 1 \leq x < \frac{2}{\sqrt3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-b9453702df77b3d58968ddd5f283cffa_l3.png)
(12) ![Rendered by QuickLaTeX.com \sqrt{x+5}-\sqrt x-\sqrt{x-3}>0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-360707956ae1c5f7a0237bcc7feeece6_l3.png)
![Rendered by QuickLaTeX.com \sqrt{x+5}-\sqrt x-\sqrt{x-3}>0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-360707956ae1c5f7a0237bcc7feeece6_l3.png)
Answer:
![Rendered by QuickLaTeX.com 3 < x < 4](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-810dadf1305e990cc9cb46e13ddb3ffd_l3.png)