Question

sa se rezolve inecuația:
$\frac{3x - 2}{4} \leqslant x - 1 \leqslant \frac{5x - 1}{2}$
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Answer 1

Răspuns:

Explicație pas cu pas:

3x -2 <= 4x -4 <= 10x -2

3x -2 <= 4x -4,  2 <= x,  x >= 2

4x-4 <= 10x -2,  -2 <= 6x , -1<= 3x,  x >= -1/3

In final  x >= 2

Answer 2

$\displaystyle \frac{3x-2}{4} \leq x-1\leq \frac{5x-1}{2} \Rightarrow 3x-2\leq 4(x-1)\leq 2(5x-1) \Rightarrow \\\\ \Rightarrow 3x-2\leq 4x-4\leq 10x-2\\\\ 3x-2\leq 4x-4 ~~~~si~~~~ 4x-4\leq 10x-2\\\\ 3x-2\leq 4x-4 \Rightarrow 3x-4x\leq -4+2 \Rightarrow -x\leq -2 \Rightarrow x\geq 2\Rightarrow x \in [2,\infty)$

$\displaystyle 4x-4\leq 10x-2 \Rightarrow 4x-10x\leq -2+4 \Rightarrow -6x\leq 2 \Rightarrow x\geq -\frac{2}{6} \Rightarrow x\geq -\frac{1}{3} \Rightarrow \\\\ \Rightarrow x \in \Bigg[-\frac{1}{3} ,\infty\Bigg)\\\\\\ x \in [2,\infty)\cap\Bigg[-\frac{1}{3} ,\infty\Bigg)=[2,\infty)~~~~~~~~~~~~~~~~~~~~~~~x\in[2,\infty)$