Solve for `x`
`(i) |x+1|=4x+3`
`(ii) |x+1|=|x+3|`
`(iii) 7|x-2|-|x-7|=5`
`(iv) ||x-1|-2|=6x+8`
`(v) |2x^(2)-3x+1|=|x^(2)+x-3|`

Solve for x (i) 2^(|x+1|)+2^(|x|)=6 and x in I (ii) x^(2)+x+1+|x-3| le |x^(2)+2x-2| (iii) |2x-4|-2|x^(2)+x-3|+2|x-1||x+1|=0

solving the following equations : (i) |x-3| = x-1 (ii) |x^(2)-3x|=2x-6 (iii) |x-4|+|x-7| = 11

solving the following equations : (i) |x-3| = x-1 (ii) |x^(2)-3x|=2x-6 (iii) |x-4|+|x-7| = 11

Factories: (i) 12x^2-7x+1 (ii) 2x^2+7x+3 (iii) 6x^2+5x-6 (iv) 3x^2-x-4

Verify by substitution that the root of . (i) 3x-5=7 is x=4 . (ii) 3+2x=9 is x=3 . (iii) 5x-8=2x-2 is x=2 . (iv) 8-7y=1 is y=1 . (v) (z)/(7)=8 is z=56 .

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

factorise (i) 2x^(3)-3x^(2)-17x+30 (ii) x^(3) -6x^(2)+11x-6 (iii) x^(3)+x^(2)-4x-4 (iv) 3x^(2)-x^(2)-3x+1

Use suitable idntities to find the following products (i) (x +5) (x +2) (ii) (x-5) (x-5) (iii) (3x +2) (3x -2) (iv) (x ^(2) + (1)/( x ^(2)) )(x ^(2) - (1)/( x ^(2))) (v) (1+x) (1+x)

Integrate the following w.r.t. x. (i) 4x^(3) , (ii) x-1/x , (iii) 1/(2x+3) , (iv) cos (4x+3) (v) cos^(2) x