{6x+2≤4x+24 ; 2x-1 ≥x+7. { 6x -4x ≤ 24 -2 ; 2x-x ≥7+1 . {2x≤22 ; x≥8.
{x≤11 ; x≥8 . ⇔x ∈[8 ;11] .
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(2x-3)(6+3x)/(7-4x) ≥0 ;
6(x+2)(x-3/2)/4(x-7/4)≤ 0 ;
(x+2)(x-3/2)/(x-7/4)≤ 0⇔{ (x+2)(x-7/4)(x-3/2) ≤ 0 ; x-7/4 ≠ 0.
- + - +
----------- [-2 ]------------ 7/4 ---------------- [3/2] --------------
x∈ ( - ∞ ; -2] U (7/4 ; 3/2] или по другому ( - ∞ ; -2] U (1,75 ; 1,5] .
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3^(2x+1) - 10*3^x+3 =0 ;
(3^x)^2) - (3+1/3)*3^x+`1 =0 ;
[3^x=1/3 ; [3^x=3⇔[ x = -1 ; x=1.
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(Loq_2 (x))² -7*Loq_2 (x ) +12 =0 ; * * * Loq_2 (x) =t ; t² -7t +12 =0 * * * *
[ Loq_2 (x )=3 ; Loq_2 (x )=4 . [ x=8 ; x=16.
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-4sin²x +5 - 4cos²x = 5 -4(sin²x +cos²x) =5 -4 =1.
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(3x² - 3)^(1/3) = (8x)^(1/3) ;
3x² - 3 = 8x ;
3x² - 8x -3 = 0 ;
x₁ = (4 -√(4² -3*(-3)) )/3 =- 1/3 ;
x₂ = (4+√(4² -3*(-3)) )/3 = 3.
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