Solve the following linear equations.
1. m – (m – 1)/2 = 1 – (m – 2)/3
2. 3(t – 3) = 5(2t + 1)
3. 8. 15(y – 4) –2(y – 9) + 5(y + 6) = 0
4. 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
5. 0.25(4f – 3) = 0.05(10f – 9)
1. m – (m – 1)/2 = 1 – (m – 2)/3
m – (m – 1)/2 = 1 – (m – 2)/3
⇒ m – m/2 – 1/2 = 1 – (m/3 – 2/3)
⇒ m – m/2 + 1/2 = 1 – m/3 + 2/3
⇒ m – m/2 + m/3 = 1 + 2/3 – 1/2
⇒ m/2 + m/3 = 1/2 + 2/3
⇒ (3m + 2m)/6 = (3 + 4)/6
⇒ 5m/6 = 7/6
⇒ m = 7/6 × 6/5
⇒ m = 7/5
2. 3(t – 3) = 5(2t + 1)
3(t – 3) = 5(2t + 1)
⇒ 3t – 9 = 10t + 5
⇒ 3t – 10t = 5 + 9
⇒ -7t = 14
⇒ t = 14/-7
⇒ t = -2
3. 15(y – 4) –2(y – 9) + 5(y + 6) = 0
15(y – 4) –2(y – 9) + 5(y + 6) = 0
⇒ 15y – 60 -2y + 18 + 5y + 30 = 0
⇒ 15y – 2y + 5y = 60 – 18 – 30
⇒ 18y = 12
⇒ y = 12/18
⇒ y = 2/3
4. 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
⇒ 15z – 21 – 18z + 22 = 32z – 52 – 17
⇒ 15z – 18z – 32z = -52 – 17 + 21 – 22
⇒ -35z = -70
⇒ z = -70/-35
⇒ z = 2
5. 0.25(4f – 3) = 0.05(10f – 9)
0.25(4f – 3) = 0.05(10f – 9)
⇒ f – 0.75 = 0.5f – 0.45
⇒ f – 0.5f = -0.45 + 0.75
⇒ 0.5f = 0.30
⇒ f = 0.30/0.5
⇒ f = 3/5
⇒ f = 0.6