Question

inecuaciones
$\sqrt{2 } - 4 < \frac{3}{2} - \frac{1}{2} x$
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Answer 1

Respuesta:

Explicación paso a paso:

$\sqrt{2}-4<\frac{3}{2}-\frac{1}{2}x\\\texttt{Sumando 1/2x a la desigualdad:}\\\\\sqrt{2}-4+\frac{1}{2}x<\frac{3}{2}-\frac{1}{2}x+\frac{1}{2}x\\\\\sqrt{2}-4+\frac{1}{2}x<\frac{3}{2}\\\texttt{Sumando}\,\,-\sqrt{2}\,\,\texttt{a la desigualdad:}\\\\\sqrt{2}-\sqrt{2}-4+\frac{1}{2}x<\frac{3}{2}-\sqrt{2}\\\\-4+\frac{1}{2}x<\frac{3}{2}-\sqrt{2}\\\texttt{Sumando 4 a ambos lados:}\\\\-4+4+\frac{1}{2}x<\frac{3}{2}-\sqrt{2}+4\\\\\frac{1}{2}x<\frac{3}{2}-\sqrt{2}+4\\\texttt{Multiplicando por 2 la desigualdad:}\\\\(2)(\frac{1}{2}x<\frac{3}{2}-\sqrt{2}+4)\\\\\frac{2}{2}x<\frac{(2)(3)}{2}-(2)\sqrt{2}+(2)(4)\\\\x<3-2\sqrt{2}+8\\\\x<3+8-2\sqrt{2}\\\\x<11-2\sqrt{2}\\\\x<8.1\\\\x<8.1=(-\infty,8.1)$

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