Solve the following linear equations.
1. x/2 – 1/5 = x/3 + 1/4
2. n/2 – 3n/4 + 5n/6 = 21
3. x + 7 – 8x/3 = 17/6 – 5x/2
4. (x – 5)/3 = (x – 3)/5
5. (3t – 2)/4 – (2t + 3)/3 = 2/3 – t
1. x/2 – 1/5 = x/3 + 1/4
x/2 – 1/5 = x/3 + 1/4
⇒ x/2 – x/3 = 1/4 + 1/5
⇒ (3x – 2x)/6 = (5 + 4)/20
⇒ 3x – 2x = 9/20 × 6
⇒ x = 54/20
⇒ x = 27/10
2. n/2 – 3n/4 + 5n/6 = 21
n/2 – 3n/4 + 5n/6 = 21
⇒ (6n – 9n + 10n)/12 = 21
⇒ 7n/12 = 21
⇒ 7n = 21 × 12
⇒ n = 252/7
⇒ n = 36
3. x + 7 – 8x/3 = 17/6 – 5x/2
x + 7 – 8x/3 = 17/6 – 5x/2
⇒ x – 8x/3 + 5x/2 = 17/6 – 7
⇒ (6x – 16x + 15x)/6 = (17 – 42)/6
⇒ 5x/6 = – 25/6
⇒ 5x = – 25
⇒ x = – 5
4. (x – 5)/3 = (x – 3)/5
(x – 5)/3 = (x – 3)/5
⇒ 5(x-5) = 3(x - 3)
⇒ 5x - 25 = 3x - 9
⇒ 5x – 3x = -9 + 25
⇒ 2x = 16
⇒ x = 8
5. (3t – 2)/4 – (2t + 3)/3 = 2/3 – t
(3t – 2)/4 – (2t + 3)/3 = 2/3 – t
⇒ ((3t – 2)/4) × 12 – ((2t + 3)/3) × 12
⇒ (3t – 2) × 3 – (2t + 3) × 4 = 2 × 4 – 12t
⇒ 9t – 6 – 8t – 12 = 8 – 12t
⇒ 9t – 6 – 8t – 12 = 8 – 12t
⇒ t – 18 = 8 – 12t
⇒ t + 12t = 8 + 18
⇒ 13t = 26
⇒ t = 2