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# RD Sharma Solutions - Ex - 8.3, Linear Equations in One Variable, Class 7, Math Class 7 Notes | EduRev

## RD Sharma Solutions for Class 7 Mathematics

Created by: Abhishek Kapoor

## Class 7 : RD Sharma Solutions - Ex - 8.3, Linear Equations in One Variable, Class 7, Math Class 7 Notes | EduRev

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.
All you need of Class 7 at this link: Class 7

#### Question 1:

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

We have
â‡’ 6x + 5 = 2x + 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.

#### Question 2:

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

We have
â‡’2(5x âˆ’ 3) âˆ’ 3(2x 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.

#### Question 3:

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.

#### Question 4:

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.

#### Question 5:

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.

#### Question 6:

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(2x + 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.

#### Question 7:

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

3x âˆ’ 2 (2x 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.

#### Question 8:

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.

#### Question 9:

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.

#### Question 10:

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.

#### Question 11:

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.

#### Question 12:

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.

#### Question 13:

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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