The document RD Sharma Solutions - Ex - 8.3, Linear Equations in One Variable, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**Solve each of the following equations. Also, verify the result in each case. 6 x + 5 = 2x + 17**

We have

â‡’ 6*x* + 5 = 2*x* + 17

Transposing 2x to LHS and 5 to RHS, we get

â‡’ 6x âˆ’- 2x = 17 âˆ’- 5

â‡’ 4x = 12

Dividing both sides by 4, we get

Verification:

Substituting x =3 in the given equation, we get

6Ã—Ã—3 + 5 = 2Ã—Ã—3 + 17

18 + 5 = 6 + 17

23 = 23

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case. 2(5 x âˆ’ 3) âˆ’ 3(2x âˆ’ 1) = 9**

We have

â‡’2(5*x* âˆ’ 3) âˆ’ 3(2*x* âˆ’ 1) = 9

Expanding the brackets, we get

â‡’ 2Ã—5x âˆ’ 2Ã—3 âˆ’3Ã—2x + 3Ã—1 = 92Ã—5x - 2Ã—3 -3Ã—2x + 3Ã—1 = 9

â‡’ 10x âˆ’ 6 âˆ’ 6x + 3 = 9

â‡’ 10x âˆ’ 6x âˆ’ 6 + 3 = 9

â‡’ 4x âˆ’ 3 = 9

Adding 3 to both sides, we get

â‡’ 4x âˆ’ 3 + 3= 9 + 3

â‡’ 4x = 12

Dividing both sides by 4, we get

Verification:

Substituting x =3 in LHS, we get

=2(5Ã—Ã—3 âˆ’ 3) âˆ’ 3(2Ã—Ã—3 âˆ’ 1)

=2Ã—Ã—12 âˆ’ 3 Ã—Ã— 5

=24 âˆ’ 15

= 9

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

Transposing x/3 to LHS, we get

X/6 =1

Multiplying both sides by 6, we get

Verification:

Substituting x = 6 in the given equation, we get

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

Transposing 2x/5 to LHS and 3/2 to RHS, we get

Multiplying both sides by 10, we get

Verification:

Substituting x = âˆ’25 in the given equation, we get

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

On expanding the brackets on both sides, we get

Transposing 3/4x to RHS and 3 to LHS, we get

Multiplying both sides by 4, we get

=> x = 9

Verification:

Substituting x = 9 on both sides, we get

6=6

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case. 3( x âˆ’ 3) = 5(2x + 1)**

6. 3(*x* âˆ’ 3) = 5(2*x* + 1)

On expanding the brackets on both sides, we get

=> 3Ã—x âˆ’ 3Ã—3 = 5Ã—2x + 5Ã—13Ã—x - 3Ã—3 = 5Ã—2x + 5Ã—1

=> 3x âˆ’- 9 = 10x + 5

Transposing 10x to LHS and 9 to RHS, we get

=> 3x âˆ’- 10x = 9 + 5

=> âˆ’-7x = 14

Dividing both sides by 7, we get

Verification:

Substituting x = âˆ’-2 on both sides, we get

3(âˆ’2âˆ’3) = 5(2(âˆ’2) +1)3-2-3 = 52-2 +1

3(âˆ’5) = 5(âˆ’3)3-5 = 5-3

âˆ’-15 = âˆ’-15

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case. 3 x âˆ’ 2 (2x âˆ’ 5) = 2(x + 3) âˆ’ 8**

**Answer 7:**

3*x* âˆ’ 2 (2*x* âˆ’ 5) = 2(*x* + 3) âˆ’ 8

On expanding the brackets on both sides, we get

=> 3xâˆ’2Ã—2x+2Ã—5 = 2Ã—x + 2Ã—3 âˆ’8

=> 3x âˆ’4x + 10 = 2x + 6 âˆ’8

=> âˆ’x + 10 = 2x âˆ’ 2

Transposing x to RHS and 2 to LHS, we get

=> 10 + 2 = 2x + x

=> 3x = 12

Dividing both sides by 3, we get

Verification:

Substituting x = 4 on both sides, we get

3(4) âˆ’ 2(2(4)âˆ’5) = 2(4+3)âˆ’834 - 224-5 = 24+3-8

12âˆ’-2 (8 âˆ’- 5) = 14âˆ’-8

12 âˆ’- 6 = 6

6 = 6

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

Transposing x/4 to LHS and âˆ’1/2 to RHS, we get

Multiplying both sides by 4, we get

Dividing both sides by 2, we get

Substituting x = 7 on both sides, we get

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

Multiplying both sides by 18, we get

Transposing 1 to RHS, we get

=> 15x = 6âˆ’-1

=> 15x = 5

Dividing both sides by 15, we get

Verification:

Substituting x = 1/3 on both sides, we get

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

Transposing m/3 to LHS and 1/2 to RHS, we get

Multiplying both sides by 6, we get

Dividing both sides by 5, we get

Verification:

Substituting m =7/5 on both sides, we get

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

Multiplying both sides by 3, we get

Subtracting 1 from both sides, we get

=> 3x + 1 âˆ’ 1 = 3 âˆ’1

=> 3x = 2

Dividing both sides by 3, we get

Verification:

Substituting x =2/3 in LHS, we get

LHS = RHS

Hence, verified.

**Solve each of the following equations. Also, verify the result in each case.**

Transposing 0.28x to LHS and 4/5 to RHS, we get

Dividing both sides by 0.32, we get

Verification:

Substituting x = 9/8 on both sides, we get

LHS = RHS

Hence, verified.

**Solve ech of the following question. Also, verify the result in each case.**

Transposing x/4 to LHS, we get

Multiplying both sides by 12, we get

Dividing both sides by 7, we get

Verification:

Substituting x = 12 on both sides, we get

LHS =RHS

Hence, verified.

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