vault backup: 2022-03-04 08:44:37

notes/.obsidian/plugins/obsidian-activity-history/data.json

@@ -12,8 +12,8 @@
   "checkpointList": [
     {
       "path": "/",
-      "date": "2022-03-03",
-      "size": 800369
+      "date": "2022-03-04",
+      "size": 801459
     }
   ],
   "activityHistory": [
@@ -495,6 +495,10 @@
         {
           "date": "2022-03-03",
           "value": 826
+        },
+        {
+          "date": "2022-03-04",
+          "value": 1264
         }
       ]
     }

notes/mat/Nerovnice.md

@@ -29,3 +29,75 @@ $$x-2\geq1(x+3)$$
 $$x-2\geq x+3 |-x+2$$
 $$0\geq5$$
 $$x=\emptyset$$
+---
+$[x\neq-1]$
+$$\frac{x-\sqrt7}{x+1} \geq 0$$
+$[x>-1]$
+$$x-\sqrt7\geq0(x+1)$$
+$$x\geq\sqrt7$$
+
+$[x<-1]$
+$$x-\sqrt7\leq0(x+1)$$
+$$x\leq0$$
+$$k=(-\infty;-1)\wedge<\sqrt7;\infty)$$
+
+---
+$$\frac{5x-3}{3x+4} \geq -1$$
+$[x\neq -\frac43]$
+$[x\lt-\frac43]$
+
+$$5x-3\geq-1(3x+4)$$
+$$5x-3\geq-3x-4$$
+$$5x\geq-3x-1$$
+$$8x\geq-1$$
+$$x\geq -\frac18$$
+$$x\in\emptyset$$
+$[x\gt-\frac43]$
+$$5x-3\le-1(3x+4)$$
+$$5x-3\le-3x-4$$
+$$5x\leq-3x-1$$
+$$8x\le-1$$
+$$x\leq-\frac18$$
+$$k=(-\frac43;-\frac18>$$
+---
+$$\frac{4x-7}{3x-2}\leq4$$
+$[x\neq-\frac23]$
+$[x\gt-\frac23]$
+$$4x-7\leq4(3x-2)$$
+$$4x-7\leq12x-8$$
+$$-7\leq8x-8$$
+$$1\leq8x$$
+$$\frac18\leq x$$
+$[x\lt-\frac23]$
+$$4x-7\ge4(3x-2)$$
+$$4x-7\ge12x-8$$
+$$-7\ge8x-8$$
+$$1\ge8x$$
+$$\frac18\ge x$$
+$$x\in\emptyset$$
+$$k=(-\frac23;\frac18>$$
+
+---
+
+$$\frac{3x-2}{4x}\leq1$$
+$[x\ne0]$
+$[x\gt0]$
+$$3x-2\leq4x$$
+$$-2\leq x$$
+$$x\in\emptyset$$
+$[x\lt0]$
+$$3x-2\ge4x$$
+$$-2\ge x$$
+$$k=(-\infty;-2>$$
+
+---
+$$\frac1{x-3}\geq\frac1{x+5}$$
+$$x+5\geq x-3$$
+$$-5\geq-3$$
+$$k=\emptyset$$
+
+---
+$$\frac{x+1}{x+3}\gt\frac{x+5}{x+6}$$
+
+---
+$$\frac{x+3}{x+5}\geq\frac{x+2}{x-1}$$