RD Sharma solution class 8 chapter 9 Linear Equation In One Variable Exercise 9.1

Exercise 9.1

Page-9.5

Question 1:

Solve each of the following equation and also verify your solution:
914=y-113

Answer 1:

914=y-113or 374+43=y or y=12712  y=12712 for the given equation. Check:L.H.S=914 R.H.S=12712-113=12712-43=127-1612=11112=914 So, L.H.S=R.H.S for y=12712

Question 2:

Solve each of the following equation and also verify your solution:
5x3+25=1

Answer 2:

5x3+25=1 5x3=1-25 5x3=35 x=35×35=925Verification:L.H.S.=53×925+25=35+2 5=1R.H.S.=1 L.H.S.=R.H.S. for x=925

Question 3:

Solve each of the following equation and also verify your solution:
x2+x3+x4=13

Answer 3:

x2+x3+x4=13 x×6+x×4+x×312=13 13x12=13 x=13×1213=12Verification:L.H.S.=122+123+124=6+4+3=13=R.H.S.

Question 4:

Solve each of the following equation and also verify your solution:
x2+x8=18

Answer 4:

x2+x8=18or 4x+x8=18or 5x8=18or x=18×85=15Verification:L.H.S.=12×15+18×15=110+140=540=18=R.H.S.

Question 5:

Solve each of the following equation and also verify your solution:
2x3-3x8=712

Answer 5:

2x3-3x8=712or 16x-9x24=712or 7x24=712or x=712×247=2Verification:L.H.S.=43-68=32-1824=712R.H.S.=712 R.H.S.=L.H.S. for x=2

Question 6:

Solve each of the following equation and also verify your solution:
(x + 2)(x + 3) + (x − 3)(x − 2) − 2x(x + 1) = 0

Answer 6:

(x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0or x2+5x+6+x2-5x+6-2x2-2x=0or 12-2x=0or x=122=6Verification:L.H.S.=(6+2)(6+3)+(6-3)(6-2)-2×6(6+1)=72+12-84=0=R.H.S.

Question 7:

Solve each of the following equation and also verify your solution:
x2-45+x5+3x10=15

Answer 7:

x2-45+x5+3x10=15or x2+x5+3x10=15+45or 5x+2x+3x10=55or 10x10=1or x=1Verification:L.H.S.=12-45+15+310=5-8+2+310=15=R.H.S.

Question 8:

Solve each of the following equation and also verify your solution:
7x+35=110

Answer 8:

7x+35=110or 7x=110-35or 7x=1-35010or x7=10-349or x=-10×7349=-70349Verification:L.H.S.=7-70349+35=7×349-70+35=349-10+35=110=R.H.S.

Question 9:

Solve each of the following equation and also verify your solution:
2x-13-6x-25=13

Answer 9:

2x-13-6x-25=13or 10x-5-18x+615=13or -8x+115=13or -24x+3=15or 24x=3-15or x=-1224=-12Verification:L.H.S.=2×-12-13-6×-12-25=-23--55=-2+33=13=R.H.S.

Question 10:

Solve each of the following equation and also verify your solution:
13(y − 4) − 3(y − 9) − 5(y + 4) = 0

Answer 10:

13(y-4)-3(y-9)-5(y+4)=0or 13y-52-3y+27-5y-20=0or 5y=45or y=455=9Verification:L.H.S.=13(9-4)-3(9-9)-5(9+4)=13×5-3×0-5×13=0=R.H.S.

Question 11:

Solve each of the following equation and also verify your solution:
23(x-5)-14(x-2)=92

Answer 11:

23(x-5)-14(x-2)=92or 2x-103-x-24=92or 8x-40-3x+612=92or 5x-3412=92or 10x-68=108or 10x=108+68or x=17610=885Verification:L.H.S.=23(885-5)-14(885-2)=23×635-14×785=92=R.H.S.

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