Solve the equations and check your answers:8 (2x – 5) – 6(3x – 7

1.	Solve the equations and check your answers:8 (2x – 5) – 6(3x – 7) = 1
Answer» Given 8 (2x – 5) – 6(3x – 7) = 1 On simplifying the brackets, we get (8 × 2x) – (8 × 5) – (6 × 3x) + (-6) × (-7) = 1 16x – 40 – 18x + 42 = 1 16x – 18x + 42 – 40 = 1 -2x + 2 = 1 Subtracting 2 from both sides, we get -2x+ 2 – 2 = 1 -2 -2x = -1 Multiplying both sides by -1, we get -2x × (-1) = -1× (-1) 2x = 1 Dividing both sides by 2, we get 2x/2 = (1/2) x = (1/2) Verification: Substituting x = (1/2) in LHS we get, (8 × 2 × (1/2)) – (8 × 5) – (6 × 3 × (1/2)) + (-6) × (-7) = 1 8(1 – 5) – 6(32 – 7) = 1 8× (-4) – (6 × 32) + (6 × 7) = 1 – 32 – 9 + 42 = 1 – 41 + 42 = 1 1 = 1 Therefore LHS = RHS Hence, verified.

Solve the equations and check your answers:8 (2x – 5) – 6(3x – 7) = 1

Answer»

Given 8 (2x – 5) – 6(3x – 7) = 1

On simplifying the brackets, we get

(8 × 2x) – (8 × 5) – (6 × 3x) + (-6) × (-7) = 1

16x – 40 – 18x + 42 = 1

16x – 18x + 42 – 40 = 1

-2x + 2 = 1

Subtracting 2 from both sides, we get

-2x+ 2 – 2 = 1 -2

-2x = -1

Multiplying both sides by -1, we get

-2x × (-1) = -1× (-1)

2x = 1

Dividing both sides by 2, we get

2x/2 = (1/2)

x = (1/2)

Verification:

Substituting x = (1/2) in LHS we get,

(8 × 2 × (1/2)) – (8 × 5) – (6 × 3 × (1/2)) + (-6) × (-7) = 1

8(1 – 5) – 6(32 – 7) = 1

8× (-4) – (6 × 32) + (6 × 7) = 1

– 32 – 9 + 42 = 1

– 41 + 42 = 1

1 = 1

Therefore LHS = RHS

Hence, verified.