The answer is: " 91 " . ___________________________________________________ → " B = 91 " . __________________________________________________
Explanation: __________________________________________________ Given: __________________________________________________ " A + B = 180 " ;
"A = -2x + 115 " ; ↔ A = 115 − 2x ;
"B = - 6x + 169 " ; ↔ B = 169 − 6x ; _____________________________________________________ METHOD 1) _____________________________________________________ Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to solve for "B" _____________________________________________________
Divide EACH SIDE of the equation by "-8 " ; to isolate "x" on one side of the equation; & to solve for "x" ;
→ -8x / -8 = -104/-8 ;
→ x = 13 __________________________________________________________ Now, to find the value of "B" : __________________________________________________________ "B = - 6x + 169 " ; ↔ B = 169 − 6x ;
↔ B = 169 − 6x ;
= 169 − 6(13) ; ===========> Plug in our "solved value, "13", for "x" ;
= 169 − (78) ;
= 91 ;
B = " 91 " . __________________________________________________ The answer is: " 91 " . ____________________________________________________ → " B = 91 " . ____________________________________________________ Now; let us check our answer: ____________________________________________________ → A + B = 180 ; ____________________________________________________ Plug in our "solved answer" ; which is "91", for "B" ; as follows: ________________________________________________________
→ A + 91 = ? 180? ;
↔ A = ? 180 − 91 ? ;
→ A = ? -89 ? Yes! ________________________________________________________ → " A = -2x + 115 " ; ↔ A = 115 − 2x ;
Plug in our solved value for "x"; which is: "13" ;
" A = 115 − 2x " ;
→ A = ? 115 − 2(13) ? ;
→ A = ? 115 − (26) ? ;
→ A = ? 29 ? Yes! _________________________________________________ METHOD 2) _________________________________________________ Given: __________________________________________________ " A + B = 180 " ;
"A = -2x + 115 " ; ↔ A = 115 − 2x ;
"B = - 6x + 169 " ; ↔ B = 169 − 6x ;
→ Solve for the value of "B" : _______________________________________________________ A + B = 180 ;
→ B = 180 − A ;
→ B = 180 − (115 − 2x) ;
→ B = 180 − 1(115 − 2x) ; ==========> {Note the "implied value of "1" } ; __________________________________________________________ Note the "distributive property" of multiplication:__________________________________________________a(b + c) = ab + ac ; <u><em>AND</em></u>: a(b − c) = ab − ac .________________________________________________________ Let us examine the following part of the problem: ________________________________________________________ → " − 1(115 − 2x) " ; ________________________________________________________
→ " − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;
= -115 − (-2x) ;
= -115 + 2x ; ________________________________________________________ So we can bring down the: " {"B = 180 " ...}" portion ;