Class 8 Linear Equations in one variable Ex 2.2

ncert solutions for class 8 maths chapter 2 exercise 2.2

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Question 1:

Solve the linear equation: \({x\over2} -{1\over5} = {x\over3}+{1\over4}\)

Answer:

\({x\over2} -{1\over5} = {x\over3}+{1\over4}\)

\({x\over2} - {x\over3}={1\over4}-{1\over5}  \)

\({3x − 2x\over 6} = {4+5\over 20} \)

\({x\over 6} = {9\over 20} \)

\(20x = 9 \times 6\)

\( x ={ 9 \times 6 \over 20}\)

\( x =2.7\)

Question 2:

Solve the linear equation: \({n\over2} - {3n\over4} + {5n\over6} = 21\)

Answer:

\({n\over2} - {3n\over4} + {5n\over6} = 21\)

\({6n − 9n + 10n\over 12} = 21\)

\( 7n = 21 \times 12\)

\( n = {21 \times 12\over 7}\)

\(n=36\)

Question 3:

Solve the linear equation: \(x+7 - {8x\over3} ={17\over6} - {5x\over2}\)

Answer:

\(x+7 - {8x\over3} ={17\over6} - {5x\over2}\)

\(x - {8x\over3}+ {5x\over2} ={17\over6} -7\)

\({6x  − 16x + 15x\over 6}= {17-42\over6}\)

\({5x\over 6} = {−25\over 6}\)

\(x = {−25 \times 6 \over 6\times 5}\)

\( x = -5\)

Question 4:

Solve the linear equation: \({x-5\over3}={x-3\over5}\)

Answer:\({x-5\over3}={x-3\over5}\)

\(5(x − 5) = 3(x − 3)\)

\( 5x − 25 = 3x − 9\)

\( 5x − 3x = 25 − 9\)

\( 2x = 16\)

\( x = {16\over 2}\)

\( x = 8\)

Question 5:

Solve the linear equation: \({3t-2\over4} - {2t+3\over3} = {2\over3}-t\)

Answer: \({3t-2\over4} - {2t+3\over3} = {2\over3}-t\)

\({(9t-6)-(8t+12)\over 12}={2-3t \over 3}\)

\({(9t-6)-(8t+12)}={(2-3t) \times 12 \over 3}\)

\( 9t − 6 − 8t − 12 = 8 − 12t \)

\( 9t − 8t + 12t = 8 + 6 + 12\)

\( 13t = 26\)

\( t = {26 \over 13}\)

\(t=2\)

Question 6:

Solve the linear equation:\(m-{(m-1)\over2}=1-{(m-2)\over3}\)

Solution: 

\(m-{(m-1)\over2}=1-{(m-2)\over3}\)

\({2m − m + 1\over 2 }= {3 − m + 2\over 3}\)

\(3 \times(2m − m + 1) = 2 \times(3 − m + 2)\)

\( 6m − 3m + 3 = 6 − 2m + 4 \)

\( 6m − 3m + 2m = 6 + 4 − 3\)

\( 5m = 7\)

\(m={7\over 5}\)

Question 7:

Simplify and solve the linear equation:3(t-3)=5(2t+1).

Answer:

\(3(t − 3) = 5(2t + 1)\)

\(3t − 9 = 10t + 5 \)

\(−9 − 5 = 10t − 3t\)

\( −14 = 7t\)

\(t={-14\over 7}\)

\(t=-2\)

Question 8:

Simplify and solve the linear equation:15(y − 4) − 2(y − 9) + 5(y + 6) = 0.

Answer:

\(15(y − 4) − 2(y − 9) + 5(y + 6) = 0\)

\(15y − 60 − 2y + 18 + 5y + 30 = 0 \)

\( 18y − 12 = 0\)

\( 18y = 12\)

\( y = {18\over12}\)

\( y = 2\over3\)

Question 9:

Simplify and solve the linear equation:3(5z − 7) − 2(9z − 11) = 4(8z − 13)−17.

Answer:

\(3(5z − 7) − 2(9z − 11) = 4(8z − 13)−17\)

\( 15z − 21 − 18z + 22 = 32z − 52 − 17\)

\( −3z + 1 = 32z − 69\)

\( −3z − 32z = −69 − 1\)

\(−35z = −70\)

\(z={-70 \over -35}\)

\( z = 2\)

Question 10:

Simplify and solve the linear equation:0.25(4f − 3) = 0.05(10f − 9).

Answer:

\(0.25(4f − 3) = 0.05(10f − 9)\)

\({25 \over 100}(4f − 3) = {5 \over 100}(10f − 9)\)

\(20(4f − 3) = 4(10f − 9)\)

\( 80f −40f  = 60− 36\)

\(40f  = 24\)

\(f = {24 \over 40}\)

\(f = {6\over 10}\)

\(f=0.6\)