а)
[tex](x - 1.2)(x + 4) \leqslant 0 \\ + + + [ - 4] - - - [1.2] + + + \\ otvet \: \: \: x \: \epsilon \:[ - 4 ; \: 1.2][/tex]
б)
[tex](2 + x)(x + 10)(3 - x) > 0 \\ (x + 2)(x + 10)(x - 3) < 0 \\ - - - ( - 10) + + + ( - 2) - - - (3) + + + \\ otvet \: \: \: x \: \epsilon\:( - \propto; \: - 10)U( - 2; \: 3)[/tex]
в)
[tex](4x + 1)(4 - 8x)(2x + 3)(7 - 4x) \geqslant 0 \\ (x + 0.25)(0.5 - x)(x + 1.5)(1.75 - x) \geqslant 0 \\ (x + 0.25)(x - 0.5)(x + 1.5)(x - 1.75) \geqslant 0 \\ + + [ - 1.5] - - [ - 0.25] + + [0.5] - - [1.75] + + \\ otvet \: \: \: x \: \epsilon \: ( - \propto; \: - 1.5] U[ - 0.25; \:0.5 ]U[1.75; \: + \propto)[/tex]
[tex] \frac{x - 4}{x + 5} > 0 \\ (x - 4)(x + 5) > 0 \\ + + + ( - 5) - - - (4) + + + \\ x \: \epsilon\:( - \propto; \: - 5)U(4; \: + \propto)[/tex]
[tex] \frac{x - 1.5}{x + 2.5} \leqslant 0 \\ (x - 1.5)(x + 2.5) \leqslant 0 \: \: \: pri \: \: x\neq - 2.5 \\ + + + ( - 2.5) - - - [1.5] + + + \\ otvet \: \: \: x \: \epsilon \: ( - 2.5; \: 1.5][/tex]
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Answers & Comments
1.
а)
[tex](x - 1.2)(x + 4) \leqslant 0 \\ + + + [ - 4] - - - [1.2] + + + \\ otvet \: \: \: x \: \epsilon \:[ - 4 ; \: 1.2][/tex]
б)
[tex](2 + x)(x + 10)(3 - x) > 0 \\ (x + 2)(x + 10)(x - 3) < 0 \\ - - - ( - 10) + + + ( - 2) - - - (3) + + + \\ otvet \: \: \: x \: \epsilon\:( - \propto; \: - 10)U( - 2; \: 3)[/tex]
в)
[tex](4x + 1)(4 - 8x)(2x + 3)(7 - 4x) \geqslant 0 \\ (x + 0.25)(0.5 - x)(x + 1.5)(1.75 - x) \geqslant 0 \\ (x + 0.25)(x - 0.5)(x + 1.5)(x - 1.75) \geqslant 0 \\ + + [ - 1.5] - - [ - 0.25] + + [0.5] - - [1.75] + + \\ otvet \: \: \: x \: \epsilon \: ( - \propto; \: - 1.5] U[ - 0.25; \:0.5 ]U[1.75; \: + \propto)[/tex]
2.
а)
[tex] \frac{x - 4}{x + 5} > 0 \\ (x - 4)(x + 5) > 0 \\ + + + ( - 5) - - - (4) + + + \\ x \: \epsilon\:( - \propto; \: - 5)U(4; \: + \propto)[/tex]
б)
[tex] \frac{x - 1.5}{x + 2.5} \leqslant 0 \\ (x - 1.5)(x + 2.5) \leqslant 0 \: \: \: pri \: \: x\neq - 2.5 \\ + + + ( - 2.5) - - - [1.5] + + + \\ otvet \: \: \: x \: \epsilon \: ( - 2.5; \: 1.5][/tex]