Find the number of integral values of x satisfying the equation: | ₂^2 x-5 ₂ x+6 |= | ₂^2 x-7 ₂ x+12 |- |2 ₂ x-6 |

Step-by-step solution

aligned & | ₂^2 x-5 ₂ x+6 |+ |2 ₂ x-6 |= | ₂^2 x-7 ₂ x+12 | & |x|+|y|=|x-y| x y 0 & ( ₂^2 x-5 ₂ x+6 ) (2 ₂ x-6 ) 0 & ( ₂ x-2 ) ( ₂ x-3 ) ( ₂ x-3 ) 0 & ( ₂ x-2 ) ( ₂ x-3 )^2 0 & ₂ x 2 or ₂ x=3 & x (0,4] 8 aligned