Which of the following equations are linear equations?
       (i) (3/2)x + 4 = 2x  – 3
       (ii) 5y – 3 = 2y  + 4 
       (iii) u + 4 = u² – 4 
       (iv) 3x + 2 = 5x – 7
      (v)  x² + 2 = x + 1  
       (vi)  y – 3 = 3y + 4
       (vii) u + 1/u = 5
       (viii) (x – 1)² = x² – 2
       (ix) (x – 1)(x – 2) = 6
       (x)  (x – 2 )(x + 3) = x + 7

(i) It is a linear equation.
(ii) It is a linear equation. 
(iii) It is not a linear equation because it is a quadratic equation. 
(iv) It is a linear equation.
(v) It is not a linear equation because it is a quadratic equation.
(vi) It is a linear equation. 
(vii) u + 1/u = 5
    .^.. u² + 1 = 5u
    It is not a linear equation because it is a quadratic equation.
(viii) (x – 1)² = x² – 2
      x² – 2x + 1 = x² – 2
      ⇒ – 2x + 1 = – 2
      ⇒ – 2x + 1 + 2 = 0
      .^.. – 2x + 3 = 0
      It is a linear equation.
(ix) (x – 1)(x – 2) = 6
      ⇒ x² + (-1 – 2)x + (-1)(-2) = 6
      ⇒ x² – 3x + 2 = 6
     ⇒ x² – 3x + 8 = 0
   It is not a linear equation because it is a quadratic equation.
(x) (x - 2 )(x + 3) = x + 7
    x² + (-2 + 3)x + (-2)(3) = x + 7
    ⇒ x² + x - 6 = x + 7 
   .^.. x² - 13 = 0
   It is not a linear equation because it is a quadratic equation.