Question

resuelve las siguientes inecuaciones x+2≤3x-5 , 3x+2> x-2/2 , x/2-x/3 >-1

Answer 1

Respuesta:

$x + 2 \leq 3x - 5\\\\=x \leq 3x - 5 - 2\\\\=x \leq 3x - 7\\\\=x - 3x \leq - 7\\\\=-2x\leq -7\\\\=x\leq \frac{-7}{-2}\\\\=x\leq \frac{7}{2}$

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$3x + 2 > x - \frac{2}{2}\\\\=3x + 2 > x - 1\\\\=3x > x - 1 - 2\\\\=3x > x -3\\\\=3x - x > -3\\\\=2x > -3\\\\=x >\frac{-3}{2}$

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$\frac{x}{2} -\frac{x}{3} > -1\\\\\=\frac{x}{2} (2+3)-\frac{x}{3}(2+3)>-1\\\\=\frac{x}{2} (6)-\frac{x}{3}(6)>-1\\\\=\frac{x}{2} (6)-\frac{x}{3}(6)>-1(6)\\\\=\frac{x(6)}{2} -\frac{x(6)}{3}>-1(6)\\\\=\frac{6x}{2}-\frac{6x}{3}> -6\\\\=3x - 2x >-6\\\\=1x > -6\\\\=x > \frac{-6}{1} \\\\=x > -6$