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Linear Equations in One Variable - 8th math

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NCERT Solution Exercise 2.3 part 1


 linear equation ncert exercise 2.3h math

Solve the following equations and check your results

Question (1) 3x = 2 x + 18

Solution: Given,

3x = 2x + 18

After transposing 2x to LHS, we get

3x-2x=18

โ‡’ x = 18 Answer

Checking of result of Result

Given equation is 3x = 2x + 18

After substituting the value of x in LHS and RHS we get:

3 x = 2 ร— 18 + 18

3 ร— 18 = 36 + 18

3 ร— 18 = 54

54 = 54

Thus, LHS = RHS

Question (2) 5t โ€“ 3 = 3t โ€“ 5

Solution:

Given, 5t โ€“ 3 = 3t โ€“ 5

After transposing 3t to LHS we get:

5t โ€“ 3 โ€“ 3t = โ€“5

After transposing โ€“3 to RHS we get

5t โ€“ 3t =โ€“5 + 3

โ‡’ 2t = โ€“2

After transposing 2 to RHS, we get

โ‡’ 2t = โ€“2/2

โ‡’ t = โ€“1 Answer

Checking of Result

Given,

5t โ€“ 3 = 3t โ€“ 5

RHS = 3t โ€“ 5

After substituting the value of t = โ€“1 which is calculated in the solution in RHS, we get

RHS = 3 ร— (โ€“1) โ€“ 5

= โ€“3 โ€“ 5

โ‡’ RHS = โ€“8

LHS = 5t โ€“ 3

After substituting the value of t = โ€“1 which is calculated in the solution in LHS, we get

LHS = 5(โ€“1) โ€“ 3

= โ€“5 โ€“ 3

โ‡’ LHS = โ€“8

Thus, LHS = RHS proved

Question (3) 5x + 9 = 5 + 3x

Solution:

Given, 5x + 9 = 5 + 3x

After transposing 9 to RHS, we get

โ‡’ 5x = 5 + 3x โ€“ 9

And, after transposing 3x to LHS, we get

โ‡’ 5x โ€“ 3x = 5 โ€“ 9

โ‡’ 2x = โ€“4

After dividing both sides by 2, we get

โ‡’ 2x/2 = โ€“4/2

โ‡’ x = โ€“2 Answer

CHECKING OF RESULT:

Given, 5x + 9 = 5 + 3x

LHS = 5x + 9

After substituting the value of x = โ€“2, we get

LHS = 5 (โ€“2) + 9

= โ€“10 + 9

โ‡’ LHS = โ€“1

Now, RHS = 5 + 3x

After substituting the value of x = โ€“2, we get

LHS = 5 + 3 (โ€“2)

= 5 + (โ€“6)

= 5 โ€“ 6

โ‡’ LHS = โ€“1

Thus, LHS = RHS Proved

Question (4) 4x + 3 = 6 + 2x

Solution:

Given, 4x + 3 = 6 + 2x

After transposing 3 to RHS, we get

4x = 6 + 2x โ€“ 3

Now, after transposing 2x to LHS, we get

4x โ€“ 2x = 6 โ€“ 3

โ‡’ 2x = 3

After dividing both sides by 2 we get

โ‡’ (2x)/2 = 3/2

โ‡’ x = 3/2 Answer

CHECKING OF RESULT:

Given, 4x + 3 = 6 + 2x

LHS = 4x + 3

Substituting the value of x = 3/2 in LHS we get

= 4 ร— 3/2 + 3

= 2 ร— 3 + 3

= 6 + 3 = 9

โ‡’ LHS = 9

Now, RHS = 6 + 2x

Substituting the value of x = 3/2 in RHS we get

= 6 + 2 ร— 3/2

= 6 + 3 = 9

โ‡’ RHS = 9

Thus, LHS = RHS proved

Question (5) 2x โ€“ 1 = 14 โ€“ x

Solution:

Given, 2x โ€“ 1 = 14 โ€“ x

After transposing โ€“1 to RHS, we get

2x = 14 โ€“ x + 1

After transposing โ€“x to LHS, we get

2x + x = 14 + 1

3x = 15

After transposing 3 to RHS, we get

x = 15/3 = 5

Thus, x = 5 Answer

CHECKING OF RESULT:

Given, 2x โ€“ 1 = 14 โ€“ x

Now, LHS =2x โ€“ 1

After substituting the value of x = 5 in LHS we get

2 ร— 5 โ€“1

= 10 โ€“ 1

Thus, LHS = 9

Now, RHS = 14 โ€“ x

After substituting the value of x = 5 in RHS we get

= 14 โ€“ 5

โ‡’ RHS= 9

Thus, LHS = RHS proved

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