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Question

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(i) 13x6=52(ii) 2x33x8=712(iii) (x+2)(x+3)+(x3)(x2)2x(x+1)=0(iv) 1107x=35(v) 13(x4)3(x9)4(x+4)=0(vi) x+78x3=17x65x8(vii) 3x242x+33=23x(viii) x+26(11x314)=3x412(ix) 25x53x=115(x) x+23x+15=x341(xi) 3x23+2x+32=x+76(xii) xx12=1x23(xiii) 9x+72(xx27)=36(xiv) 6x+12+1=7x33

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Solution

(i) 13x6=52 13x=52+61 13x=5×12×1+6×21×2 13x=52+122 13x=5+122=13x=172.=x=17×32×1=512=2512(ii) 2x33x8=71223,823,423,233,11 L.C.M. of 3 and 8 =2×2×2×3=24 2x×83×83x×88×3=712=16x249x24=712=16x9x24=712=7x24=712=x=7×2712×7=2 x=2(iii) (x+2)(x+3)+(x3)(x2)2x(x+1)=0 [x2+(2+3)x+2×3]+[x2+(32)x+(3)(2)]2x22x=0 x2+5x+6+x25x+62x22x=0 x2+x22x2+5x5x2x+6+6=0=2x+12=0Subtracting 12 from both sides,2x+1212=012 2x=12Dividing by -22x2=122 x=6 x=6VerificationL.H.S.=(x+2)(x+3)+(x3)(x2)2x(x+1)=(6+2)(6+3)+(63)(62)2×6(6+1)=8×9+3×412×7=72+1284=8484=0=R.H.S.(iv) 1107x=35 7x=35110 7x=35×101×101×110×1 7x=350110 1x=350110×(7) x=349(70)=70349(v) 13(x4)3(x9)4(x+4)=0 13(x4)3(x9)5(x+4)=0 13x523x+275x20=0 13x3x5x52+2720=0 13x8x72+27=0 5x45=0Dividing by 5,5x5455=0 x9=0 x=9Verification,~L.H.S. =13(x4)3(x9)5(x+4)=13(94)3(99)5(9+4)=13×53×05×13(vi) x+78x3=17x65x8 3(x+7)8x3=17x×45x×324 3x+218x3=68x15x24 5x+213=53x24 3×53x=24(5x+21) 159x=120x+504 159x+120x=504 279x=504 x=504279=16893=5661 x=12531(vii) 3x242x+33=23x=3x242x+33=23x1=3(3x2)4(2x+3)12=2×13×1x×31×3=9x68x1212=23x3=(x18)12=23x3=3(x18)=12(23x)=3x54=2436x=3x+36x=24+54=39x=78x=7839=2 x=2(viii) x+26(11x314)=3x412 x+26(4(11x)1×312)=3x412 x+2644+4x+312=3x412 2(x+2)41+4x12=3x412 2x+441+4x12=3x412 6x3712=3x412 12(6x37)=12(3x4) 72x444=36x48 72x36x=48+444 36x=396 x=39636=11 x=11(ix) 25x53x=11525x53x=115 2×35x×35×53x×5=115 62515x=115 1915x=115 19x=1515 19=x x=19(x) x+23x+15=x341 (L.C.M. of 3 and 5 = 15) 5(x+2)3(x+1)15=x344 5x+103x315=x74 2x+715=x74 4(2x+7)=15(x7) 8x+28=15x105 8x15x=133x=1337 x=19(xi) 3x23+2x+32=x+76 2(3x2)+3(2x+3)6=x+76 6x4+6x+96=6x+76 12x+56=6x+76 6(12x+5)=6(6x+7) 72x+30=36x42 72x36x=4230 36x=12x=1236 x=13(xii) xx12=1x23 2(x)1(x1)2=3(1)1(x2)3 2xx+12=3x+23 1x+12=5x3 3(x+1)=2(5x) 3x+3=102x 3x+2x=103 5x=7 x=75(xiii) 9x+72(xx27)=36 9x+72(7×x1(x2)7)=36 9x+72(7xx27)=36 9x+72(6x27)=36 7(9x+7)+2(6x+2)14=36 63x+4912x+414=36 51x+5314=36 51x+53=14×36 51x=50453 51x=459 x=45951 x=9(xiv) 6x+12+1=7x33 (6x+1)2+1=7x33 6x+1+22=7x33 6x+32=7x33 3(6x+3)=2(7x3) 18x+9=14x6 18x14x=69 4x=15 x=154


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