Question

Срочно алгебра 10 клас

Answer 1

1)

$\displaystyle |x-1|\leq 1,2\\\\\left \{ {{x-1\leq1,2 } \atop {x-1\geq 0 }} \right. \\\\\left \{ {{x\leq 2,2} \atop {x\geq1 }} \right. \\x\in\Big[1;\:2,2\Big]\\\\\left \{ {{-x+1\leq1,2 } \atop {x-1<0}} \right. \\\\\left \{ {{x\geq- 0,2} \atop {x<1}} \right. \\x\in\Big[-0,2; \:1\Big)$

$x\in\Big[-0,2;\:2,2\Big]$

2)

$\displaystyle |x-1|\geq 3\\\left \{ {{x-1\geq3 } \atop {x-1\geq0 }} \right. \\\\\left \{ {{x\geq4 } \atop {x\geq0 }} \right. \\x\in\Big[0; \: +\infty\Big)\\\\\left \{ {{-x+1\geq3 } \atop {x-1<0}} \right. \\\\\left \{ {{x\leq-2 } \atop {x<1}} \right. \\\\x\in (-\infty; \: -2] \cup [4;\: +\infty)$

3)

$\displaystyle |7x+5|<2\\\\\left \{ {{7x+5<2} \atop {7x+5\geq0 }} \right. \\\left \{ {{x<-\dfrac{3}{7} } \atop {x\geq-\dfrac{5}{7} }} \right. \\\\\left \{ {{-7x-5<2} \atop {7x+5<0}} \right. \\\\\left \{ {{x>-1} \atop {x<-\dfrac{5}{7} }} \right. \\x\in\Big(-1;\:-\frac{3}{7} \Big)$

4)

$\displaystyle |5-4x|>6\\\left \{ {{5-4x>6} \atop {5-4x\geq0 }} \right. \\\\\left \{ {{x<-\dfrac{1}{4} } \atop {x\leq \dfrac{5}{4} }} \right. \\\\\left \{ {{-5+4x>6} \atop {5-4x<0}} \right. \\\\\left \{ {{x>\dfrac{11}{4} } \atop {x>\dfrac{5}{4} }} \right. \\x\in\Big(-\infty;\:-0,25)\cup(2,75;\:+\infty)$

5)

$\displaystyle |3x-6|<x-1\\|3x-6|-x<-1\\\\\left \{ {{3x-6-x<-1} \atop {3x-6\geq0 }} \right. \\\\\left \{ {{x<\dfrac{5}{2} } \atop {x\geq2 }} \right. \\\\\left \{ {{-3x+6-x<-1} \atop {3x-6<0}} \right. \\\\\left \{ {{x>\dfrac{7}{4} } \atop {x<2}} \right. \\x\in\Big(1,75;\: 2,5\Big)$