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1. Solution: (1) When 2x+3 0, x-4<0, the solution is -3 2 x<4
When 2x+3 0, x-4>0, no solution.
2) When 3(x+1)>0, 2x-1 3(x+1), the solution is x>-1, x -4, and there is no solution.
When 3(x+1) < 0, 2x-1 3(x+1) gives -4 x<-1
3) When 1-3x>0, x-2<0, the solution is x<1 3
When 1-3x<0, x-2>0, the solution is x<2
4) When x-3>0, 3x+1 x-3, the solution is x>3, x -2, so x>3
When x-3<0, 3x+1 x-3, the solution is x<3, x -2, so x -2
2. Solution: (1) When 5x-4 0, 5x-4<6, the solution is 4 5 x<2;When 5x-4<0, -(5x-4)<6, the solution is -2 58, and there is no solution.
3) When 2x-3 0, 2x-3>2, the solution is 5 22, and the solution is x<1 2
4) When x-2 0, 3(x-2)-1>0, the solution is x>7 3;When x-2<0, -3(x-2)-1>0, the solution is x<5 3
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(3x+1)/(x-3)≥1
Solution: When x 3 0, 3x 1 x 3 0, solution x 3
When x-3 0, 3x 1 x-3 0, solution x 2
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Shift (3x+1) (x-3)-1 0
Score (3x+1-x+3) (x-3) 0
2(x+2)/(x-3)≥0
Multiplication of both sides (x-3).
Apparently (X-3) >0
So the unequal sign remains the same.
2(x+2)(x-3)≥0
x≤-2,x≥3
The denominator is x-3≠0
So x -2, x > 3
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If the denominator is greater than zero, multiply it directly to the right of the inequality, and then move the unknowns to the left, just find it.
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When (3x+1-x+3) (x-3) =0,x≠3(2x+4) (x-3) =0,x≠3(2x+4) *x-3)=0, the two solutions are x= = larger value, = smaller value, and x≠3
Get the solution of the inequality: x 3 or x = -2
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The root equation b -4ac=1-12=-11<0 has no solution.
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