\nEnunciado<\/b><\/span><\/p>\n
Considera as seguintes inequa\u00e7\u00f5es:<\/p>\n
$$\\begin{matrix}
\n6x-2<0 & {} & -4x\\ge -2 & {} & -3x+2>1\u00a0 \\\\
\n\\end{matrix}$$<\/p>\n
- \n
- Resolve cada uma delas, apresentando a solu\u00e7\u00e3o na forma de intervalo.<\/li>\n
- Os n\u00fameros $\\frac{1}{3}$ e $-\\frac{1}{3}$ s\u00e3o solu\u00e7\u00f5es comuns \u00e0s tr\u00eas inequa\u00e7\u00f5es? Justifica.<\/li>\n<\/ol>\nResolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n
- \n
- 1.\u00aa inequa\u00e7\u00e3o<\/strong>:
\n$$\\begin{array}{*{35}{l}}
\n6x-2<0 & \\Leftrightarrow\u00a0 & 6x<2\u00a0 \\\\
\n{} & \\Leftrightarrow\u00a0 & x<\\frac{1}{3}\u00a0 \\\\
\n\\end{array}$$
\n\\[{{S}_{1}}=\\left] -\\infty ,\\frac{1}{3} \\right[\\]2.\u00aa inequa\u00e7\u00e3o<\/strong>:
\n$$\\begin{array}{*{35}{l}}
\n-4x\\ge -2 & \\Leftrightarrow\u00a0 & x\\le \\frac{1}{2}\u00a0 \\\\
\n\\end{array}$$
\n\\[{{S}_{2}}=\\left] -\\infty ,\\frac{1}{2} \\right]\\]3.\u00aa inequa\u00e7\u00e3o<\/strong>:
\n$$\\begin{array}{*{35}{l}}
\n-3x+2>1 & \\Leftrightarrow\u00a0 & -3x>-1\u00a0 \\\\
\n{} & \\Leftrightarrow\u00a0 & x<\\frac{1}{3}\u00a0 \\\\
\n\\end{array}$$
\n\\[{{S}_{3}}=\\left] -\\infty ,\\frac{1}{3} \\right[\\]<\/li>\n- Os n\u00fameros $\\frac{1}{3}$ e $-\\frac{1}{3}$ n\u00e3o s\u00e3o solu\u00e7\u00f5es comuns \u00e0s tr\u00eas inequa\u00e7\u00f5es, pois, ainda que $-\\frac{1}{3}$ seja solu\u00e7\u00e3o das tr\u00eas inequa\u00e7\u00f5es, $\\frac{1}{3}$ apenas \u00e9 solu\u00e7\u00e3o da 2.\u00aa inequa\u00e7\u00e3o.<\/li>\n<\/ol>\n
\u00a0
![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag113-7.gif\" "\\"Reta")
<\/a><\/p>\n - Os n\u00fameros $\\frac{1}{3}$ e $-\\frac{1}{3}$ n\u00e3o s\u00e3o solu\u00e7\u00f5es comuns \u00e0s tr\u00eas inequa\u00e7\u00f5es, pois, ainda que $-\\frac{1}{3}$ seja solu\u00e7\u00e3o das tr\u00eas inequa\u00e7\u00f5es, $\\frac{1}{3}$ apenas \u00e9 solu\u00e7\u00e3o da 2.\u00aa inequa\u00e7\u00e3o.<\/li>\n<\/ol>\n
- 1.\u00aa inequa\u00e7\u00e3o<\/strong>: