Chapter 8: Linear Equations in One Variable Exercise – 8.3
Question: 1
6x + 5 = 2x + 17
Solution:
We have
6x + 5 = 2x+ 17
Transposing 2x to LHS and 5 to RHS, we get
6x – 2x = 17 – 5
4x = 12
Dividing both sides by 4, we get
4x/4 = 12/4
x = 3
Verification:
Substituting x = 3 in the given equation, we get
6 × 3 + 5 = 2 × 3 + 17
18 + 5 = 6 + 17
23 = 23
LHS = RHS
Hence, verified.
Question: 2
2(5x – 3) -3(2x – 1) = 9
Solution:
We have
2(5x – 3) – 3(2x – 1) = 9
Expanding the brackets, we get
2 × 5x – 2 × 3 – 3 × 2x + 3 × 1 = 9
10x – 6 - 6x + 3 = 9
10x – 6x – 6 + 3 = 9
4x – 3 = 9
Adding 3 to both sides, we get
4x – 3 + 3 = 9 + 3
4x = 12
Dividing both sides by 4, we get
4x/4 = 12/4
Thus, x = 3.
Verification:
Substituting x = 3 in LHS, we get
= 2(5 × 3 – 3) – 3(2 × 3 – 1)
= 2 × 12 – 3 × 5
= 24 – 15
= 9
LHS = RHS
Hence, verified.
Question: 3
Solution:
3 = 2 + 1
3 = 3
LHS = RHS
Hence, verified.
Question: 4
Solution:
LHS = RHS
Hence, verified.
Question: 5
Solution:
On expanding the brackets on both sides, we get
Question: 6
3(x – 3) = 5(2x + 1)
Solution:
3(x – 3) = 5(2x + 1)
On expanding the brackets on both sides, we get
= 3 × x – 3 × 3 = 5 × 2x + 5 × 1
= 3x – 9 = 10x + 5
Transposing 10x to LHS and 9 to RHS, we get
= 3x – 10x = 9 + 5
= -7x = 14
Dividing both sides by 7, we get
= –7x/7 = 14/7
=x = -2
Verification:
Substituting x = -2 on both sides, we get
3(-2 – 3) = 5{2(-2) +1}
3(-5) = 5(-3)
-15 = -15
LHS = RHS
Hence, verified.
Question: 7
3x – 2(2x – 5) = 2(x + 3) – 8
Solution:
3x – 2(2x – 5) = 2(x + 3) – 8
On expanding the brackets on both sides, we get
= 3x – 2 × 2x + 2 × 5 = 2 × x + 2 × 3 – 8
= 3x – 4x + 10 = 2x + 6 – 8
= -x + 10 = 2x – 2
Transposing x to RHS and 2 to LHS, we get
= 10 + 2 = 2x + x
= 3x = 12
Dividing both sides by 3, we get
= 3x/3 = 12/3
= x = 4
Verification:
Substituting x = 4 on both sides, we get
3(4) – 2{2(4) – 5} = 2(4 + 3) – 8
12 – 2(8 – 5) = 14 – 8
12 – 6 = 6
6 = 6
LHS = RHS
Hence, verified.
Question: 8
Solution:
Transposing x/4 to LHS and – (1/2) to RHS, we get
Multiplying both sides by 4, we get
Dividing both sides by 2, we get
= 2x/2 = 14/2
= x = 7
Verification:
Substituting x = 7 on both sides, we get
Question: 9
Solution:
Multiplying both sides by 18, we get
Transposing 1 to RHS, we get
= 15x = 6 – 1
= 15x = 5
Dividing both sides by 15, we get
= 15x/15 = 5/15
=x = 1/3
Verification :
Substituting x = 1/3 both sides, we get
LHS = RHS
Hence, verified.
Question: 10
Solution:
Dividing both sides by 5, we get
= 5m/5 = 7/5
= m = 7/5
Verification:
Substituting m = 75 on both sides, we get
LHS = RHS
Hence, verified.
Question: 11
Solution:
Multiplying both sides by 3, we get 3
Subtracting 1 from both sides, we get
= 3x + 1 – 1 = 3 – 1
= 3x = 2
Dividing both sides by 3, we get
= 3x + 1 - 1 = 3 -1
= 3x = 2
Dividing both sides by 3, we get
= 3x/3 = 2/3
= x = 2/3
Verification:
Substituting x = 2/3 in LHS, we get
= RHS
LHS = RHS Hence, verified.
Question: 12
0.6x + 4/5 = 0.28x + 1.16
Solution:
0.6x + 4/5 = 0.28x + 1.16
Transposing 0.28x to LHS and 45 to RHS, we get
= 0.6x – 0.28x = 1.16 – 45
= 0.32x = 1.16 – 0.8
= 0.32x = 0.36
Dividing both sides by 0.32, we get
= 0.32 x 0.32 = 0.360.32
= x = 98
Verification:
Substituting x = 98 on both sides, we get
0.6(9/8) + 45 = 0.28(9/8) + 1.16
5.4/8 + 4/5 = 2.52/8 + 1.16
0.675 + 0.8 = 0.315 + 1.16
1.475 = 1.475
LHS = RHS
Hence, verified.
Question: 13
0.5x + x/3 = 0.25x + 7
Solution:
0.5x + x/3 = 0.25x + 7
Transposing x/4 to LHS, we get
Multiplying both sides by 12, we get
= x = 12
Verification:
Substituting x = 12 on both sides, we get
0.5(12) + (12)3 = 0.25(12) + 7
6 + 4 = 3 + 7
10 = 10
LHS = RHS
Hence, verified.