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# 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

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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)

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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

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