The answer is: " 8 " . ________________________________ Explanation: ________________________________ Let "x" represent the "original number".
2(x - 3) = 6 + (1/2)x ; Solve for "x" ; ______________________________________ Multiple the ENTIRE EQUATION (both sides) by "2" ; to get rid of the fraction:
2*{2(x - 3) = 6 + (1/2)x} ;
to get:
4(x - 3) = 12 + x ; ___________________________ Let us expand the "left-hand side" of the equation: _____________________________________________ Note the "distributive property of multiplication" : _____________________________________________ a(b - c) = ab - ac ; a(b +c) = ab + ac ; ______________________________________________ So; "4(x - 3)" = 4*x - 4*3 = 4x - 12 ; ______________________________________________ Rewrite the equation: _______________________________________________ 4x - 12 = 12 + x ;
Subtract "x" from EACH side of the equation; and Add "12" to EACH SIDE OF THE EQUATION; ______________________________________________ 4x - 12 - x + 12 = 12 + x - x + 12 ;
to get: ______________________________________________ 3x = 24 ; _____________________________________________ Now, divide EACH side of the equation by "3" ; to isolate "x" on one side of the equation; and to solve for "x" ; _____________________________________________ 3x/3 = 24/3 ; _____________________________________________ x = 8 . _____________________________________________
