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5-1/2x=5/8x+2

  x = 8/3 ; or, write as:  2 2/3; or, write as, 2.66666667 .

Explanation:


 Given:   5 − 1/2 x = 5/8 x + 2 ;

    Change the  1/2 x  to "4/8 x" ;

Since "1/2" = "(1*4)/(2*4)" = "(4/8)"; and rewrite:

      → 5 − (4/8)x = (5/8)x + 2 ;

  Subtract "5"; and add "(5/8)x" to EACH side of the equation:

 5 − (4/8)x  −  5 + (5/8)x  =  (5/8)x  + 2 − 5 + (5/8)x ;

to get:

                 (1/8) x = (10/8)x  − 3

Multiply the entire equation (BOTH SIDES) by "8"; to get rid of the fraction:


8 * { (1/8) x = (10/8)x − 3 }; 

     to get:

              x = 10x − 24 ;

Subtract "x" ; and add "24" ; to EACH side of the equation:

       →      x − x + 24 =  10x − 24  − x  + 24 ;

       to get:

            →  24  = 9x ; ↔  9x = 24 ;

  → Divide EACH side of the equation by "9" ; to isolate "x" on one side of the equation; and to solve for "x" ;

        → 9x / 9 = 24 / 9 ;

        →    x = 24/9 = (24÷3)/ (9÷3) = 8/3

        →    x = 8/3 ; or, write as:  2 2/3; or, write as, 2.66666667.

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