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Solve the following equations and check your results. 1. 8x + 4 = 3 (x – 1) + 7 2. x = 4/5 (x + 10) 3. 2x/3 + 1 = 7x/15 + 3 4. 2y + 5/3 = 26/3 – y 5. 3m = 5m – 8/5

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Solve the following equations and check your results.

1. 8x + 4 = 3 (x – 1) + 7

2. x = 4/5 (x + 10)

3. 2x/3 + 1 = 7x/15 + 3

4. 2y + 5/3 = 26/3 – y

5. 3m = 5m – 8/5

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1. 8x + 4 = 3 (x – 1) + 7

8x + 4 = 3 (x – 1) + 7

⇒ 8x + 4 = 3x – 3 + 7

⇒ 8x + 4 = 3x + 4

⇒ 8x – 3x = 4 – 4

⇒ 5x = 0

⇒ x = 0

Putting the value of x in RHS and LHS we get,

(8 × 0) + 4 = 3 (0 – 1) + 7

⇒ 0 + 4 = 0 – 3 + 7

⇒ 4 = 4

⇒ LHS = RHS

2. x = 4/5 (x + 10)

x = 4/5 (x + 10)

⇒ x = 4x/5 + 40/5

⇒ x – (4x/5) = 8

⇒ (5x – 4x)/5 = 8

⇒ x = 8 × 5

⇒ x = 40

Putting the value of x in RHS and LHS we get,

40 = 4/5 (40 + 10)

⇒ 40 = 4/5 × 50

⇒ 40 = 200/5

⇒ 40 = 40

⇒ LHS = RHS

3. 2x/3 + 1 = 7x/15 + 3

2x/3 + 1 = 7x/15 + 3

⇒ 2x/3 – 7x/15 = 3 – 1

⇒ (10x – 7x)/15 = 2

⇒ 3x = 2 × 15

⇒ 3x = 30

⇒ x = 30/3

⇒ x = 10

Putting the value of x in RHS and LHS we get,

(2 x 10)/3 + 1 = (7 x 10)/15 + 3

⇒ 20/3 + 1 = 70/15 + 3

⇒ 23/3 = 115/15

⇒ 23/3 = 23/3

⇒ LHS = RHS

4. 2y + 5/3 = 26/3 – y

2y + 5/3 = 26/3 – y

⇒ 2y + y = 26/3 – 5/3

⇒ 3y = (26 – 5)/3

⇒ 3y = 21/3

⇒ 3y = 7

⇒ y = 7/3

Putting the value of y in RHS and LHS we get,

⇒ (2 × 7/3) + 5/3 = 26/3 – 7/3

⇒ 14/3 + 5/3 = 26/3 – 7/3

⇒ (14 + 5)/3 = (26 – 7)/3

⇒ 19/3 = 19/3

⇒ LHS = RHS

5. 3m = 5m – 8/5

3m = 5m – 8/5

⇒ 5m – 3m = 8/5

⇒ 2m = 8/5

⇒ 2m × 5 = 8

⇒ 10m = 8

⇒ m = 8/10

⇒ m = 4/5

Putting the value of m in RHS and LHS we get,

⇒ 3 × (4/5) = (5 × 4/5) – 8/5

⇒ 12/5 = 4 – (8/5)

⇒ 12/5 = (20 – 8)/5

⇒ 12/5 = 12/5

⇒ LHS = RHS

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