Dear student x2-5x+6>x-2For x-2≥0 ,x≥2, So, for x≥2 , x-2=x-2For x-2 -x-2 x2-5x+6>-x+2x2-4x+4>0x-22>0⇒x>2 or x x-2x2-6x+8=0x-4x-2>0Computing the signs of x-4x-2For x-4x-4 is zero for x=4x-4 is negative for x 4For x-2x-2 is zero for x=2x-2 is negative for x 2 Choosimng the ranges that satisfy required condition : >0x 4Combining the rangesx 4Interval notation:-∞,2∪4,∞ Regards

14 question????

14 question???? 014. - is T alue of z, Iz +31 > 12z —II is QI 6. The solution set of the inequality - 16)

Dear student

x^{2} - 5 x + 6 > |x - 2| For x - 2 \geq 0, x \geq 2, So, for x \geq 2, |x - 2| = x - 2 For x - 2 < 0, x < 2 So, for x < 2, |x - 2| = - (x - 2) ie x < 2, x \geq 2 For x < 2 x^{2} - 5 x + 6 > (- (x - 2)) x^{2} - 5 x + 6 > - x + 2 x^{2} - 4 x + 4 > 0 {(x - 2)}^{2} > 0 \Rightarrow x > 2 or x < 2 For x \geq 2 x^{2} - 5 x + 6 > x - 2 x^{2} - 6 x + 8 = 0 (x - 4) (x - 2) > 0 Computing the signs of (x - 4) (x - 2) For x - 4 x - 4 is zero for x = 4 x - 4 is negative for x < 4 x - 4 is positive for x > 4 For x - 2 x - 2 is zero for x = 2 x - 2 is negative for x < 2 x - 2 is positive for x > 2

Choosimng the ranges that satisfy required condition : > 0 x < 2 or x > 4 Combining the ranges x < 2 or x > 4 Interval notation : (- \infty, 2) \cup (4, \infty)

Regards

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14 question???? 14 question???? 014. - is T alue of z, Iz +31 > 12z —II is QI 6. The solution set of the inequality - 16)

14 question????

14 question???? 014. - is T alue of z, Iz +31 > 12z —II is QI 6. The solution set of the inequality - 16)