Verified answer

OTBET: x∈(-2;3¹/₃).

Объяснение:

[tex]|12-2x| > |4x-8|\\[/tex]

Найдём нули функции:

[tex]\displaystyle\\\left \{ {{12-2x=0} \atop {4x-8=0}} \right. \ \ \ \ \ \left \{ {{12=2x\ |:2} \atop {4x=8\ |:4}} \right. \ \ \ \ \ \left \{ {{x=6} \atop {x=2}} \right. \ \ \ \ \ \Rightarrow[/tex]

-∞____2____6____+∞

    x∈(-∞;2)

[tex]12-2x > -(4x-8)\\12-2x > -4x+8\\4x-2x > 8-12\\2x > -4 |:2\\x > -2 \ \ \ \ \ \Rightarrow\\x\in(-2,2)\\[/tex]

    x∈[2,6]

[tex]\displaystyle\\12-2x > 4x-8\\12+8 > 4x+2x\\20 > 6x\ |:6\\\frac{10}{3} > x \\x < 3\frac{1}{3} \ \ \ \ \ \Rightarrow\\\\x\in[2;3\frac{1}{3} )\\[/tex]

    x∈(6;+∞)

[tex]-(12-2x) > 4x-8\\-12+2x > 4x-8\\-12+8 > 4x-2x\\-4 > 2x\ |:2\\-2 > x\\x < -2\\x\notin(6;+\infty) \ \ \ \ \ \ \ \Rightarrow\\\\x\in(-2;3\frac{1}{3} )[/tex]