1. 2x + 1 = 9
⇒ 2x = 9 – 1 = 8 (Shifting 1 to other side)
⇒ 2x/2 = 8/2 ⇒ x = 4
Verification of answer
LHS = 2x +1
= 2 x 4 + 1
= 8 + 1
= 9 = RHS
So, x = 4 is correct answer.
2. 5x – 4 = 26
⇒ 5x = 26 + 4 (Transferring side)
⇒ 5x = 30
⇒ 5x/5 = 30/5
⇒ x = 6
Verification of answer
LHS = 5x – 4
= 5 x 6 – 4 = 30 – 4
= 26 = RHS
So x = 6 is correct answer.
3. 5x – 2x + 7 = 31
3x + 7 = 31
⇒ 3x = 31 – 7 (Transferring side)
3x = 24
⇒ 3x/3 = 24/3 (Dividing both sides by 3)
x = 8
Verification of answer
LHS = 5x – 2x + 7
= 5 x 8 – 2 x 8 + 7
= 40 – 16 +7 = 31 = RHS
So x = 8 is correct answer.
4. 5x + 8 = 12 + 6
⇒ 5x = 18 – 8 = 10 (shifting 8 to other side)
⇒ 5x/5 = 10/5 (Dividing both sides by 5)
⇒ x = 2
Verification of answer
LHS = 5x + 8
= 5 x 2 + 8 = 18
RHS = 12 + 6 = 18
So x = 2 is correct answer.
5. 12x + 3x = 60
⇒ 15 = 60
⇒ 15x/5 = 60/15 = 4 (Dividing by 15 both sides)
⇒ x = 4
Verification of answer
LHS = 12x + 3x = 15x
= 15 x 4 = 60 = RHS
So x = 4 is correct answer.
12. 6z + 10 = -2
⇒ 6z = -2 – 10
⇒ 6z = -12
z = – 12/6 = -2
Verification of answer
LHS = 6z + 10
= 6 x (-2) + 10
= -12 + 10
= -2 = RHS
So z = -2 is correct answer.
13. q/4 + 7 = 5
⇒ q/4 = 5 – 7 = -2
q = -2 x 4 = -8
Verification of answer
LHS = q/4 + 7 = -8/4 + 7
= -2 +7 = 5 = RHS
So q = -8 is correct answer.
14. 4(2 – x) = 8
⇒ 2 – x = 8/4
⇒ 2 – x = 2
⇒ x = 2 – 2 = 0
Verification of answer
LHS = 4(2 – x)
= 4(2 – 0) = 8 = RHS
So x = 0 is correct answer.
15. 3(n -5) = 21
⇒ n – 5 = 21/3 = 7
⇒ n = 7 + 5 = 12
Verification of answer
LHS = 3(n – 5)
= 3(12 – 5) = 3(7)
= 21 = RHS
So n = 12 is correct answer.
17. 0 = 16 + 4(m – 6)
⇒ 16 + 4(m – 6) = 0
⇒ 4(m – 6) = -16
⇒ m – 6 = -16/4 = -4
⇒ m = -4 + 6 = 2
Verification of answer
RHS = 16 + 4(m – 6)
= 16 + 4(2 – 6)
= 16 + 4(-4)
= 16 – 16 = 0 = LHS
So m = 2 is correct answer.