Question

алгебра 8 класс, номер 1015

Answer 1

а) $left { {{10,9 - 2x textless 0} atop {12x-90 textless x}} right.$

$left { {{2x textgreater 10,9} atop {12x-x textless -90}} right.$

$left { {{x textgreater 5,45} atop {11x textless 90}} right.$

$left { {{x textgreater 5,45} atop {11x textless 8 frac{2}{11}}} right.$

x∈ (5,45 ; $8 frac{2}{11}$). Целые решения: 6, 7, 8

б) $left { {{1-3x textless 3} atop {6-2x geq 0}} right.$

$left { {{-3x textless 2} atop {-2x geq -6}} right.$

$left { {{x textgreater - frac{2}{3}} atop {x leq 3}} right.$

x∈ ($-frac{2}{3}$ ; 3]. Целые решения: 0, 1, 2, 3

в) $left { {{(x+3)^3 textgreater x^2(x+9)} atop {37-12x textgreater 0}} right.$

$left { {{x^3+9x^2+27x+27-x^3-9x^2 textgreater 0} atop {37-12x textgreater 0}} right.$

$left { {{27x textgreater -27} atop {-12x textgreater -37}} right.$

$left { {{x textgreater -1} atop {x textless 3 frac{1}{12}}} right.$

x∈ (-1 ; $3frac{1}{12}$). Целые решения: 0, 1, 2, 3

г) $left { {{(4-x)^3-x^2(12-x) textless 0} atop {7-3x textgreater 0}} right.$

$left { {{(64-3*16*x+3*4*x^2-x^3) -12x^2+x^3 textless 0} atop {7-3x textgreater 0}} right.$

$left { {{64-48x+12x^2-x^3 -12x^2+x^3 textless 0} atop {7-3x textgreater 0}} right.$

$left { {{-48x textless -64} atop {-3x textgreater -7}} right.$

$left { {{x textgreater 1 frac{1}{3}} atop {x textless 2 frac{1}{3} }} right.$

x∈ (1 frac{1}{3}} ; 2 frac{1}{3}). Целое решение: 2.