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. _______________________________________________________
