Answers: _________________________________________________________ Question 1) The correct answer is: [C]: " 5 " . _________________________________________________________ Question 2) The correct answer is: [C]: "-24 " .
_________________________________________________________ Explanation: _____________________________________________ Question #1) _____________________________________________ The "denominator" must not equal "zero" ; since one cannot "divide by zero" ;
As such, the value of the "denominator"; which is: "(9x − 45)" ; cannot equal "zero".
So, what is the value of "x" when: "9x − 45 = 0" ? ; __________________________________________________ Method 1) __________________________________________________
" 9x − 45 = 0 " ; Solve for "x" ;
Add "45" to each side of the equation;
9x − 45 + 45 = 0 + 45 ;
to get:
9x = 45 ;
Divide each side of the equation by "9" ; to isolate "x" on one side of the equation; & to solve for "x" ;
9x / 9 = 45 / 9 ;
x = 5 ; which is: Answer choice: [C]: "5" . ________________________________________________ Method 2)
" 9x − 45 = 0 " ; Solve for "x" ;
→ Factor out a "9" in: " 9x − 45" ; and rewrite:
→ " 9(x − 5) = 0 " ;
Divide EACH SIDE of the equation by "9" ;
→ " { [9(x − 5)] / 9 } = { 0 / 9 } ;
→ x − 5 = 0 ;
Add "5" to EACH SIDE of the equation; to isolate "x" on one side of the equation; & to solve for "x" ;
→ x − 5 + 5 = 0 + 5 ;
→ x = 5 ; which is: Answer choice: [C]: " 5 " . _________________________________________________________
Question #2) _________________________________________________________ Again, note that the "denominator" must not equal "zero" ; since one cannot "divide by zero" ;
As such, the value of the "denominator"; which is: "2x + 48" ; cannot equal "zero".
So, what is the value of "x" when: "2x + 48 = 0" ? ; _______________________________________________________ Method 1) _______________________________________________________ " 2x + 48 = 0 " ; Solve for "x" ;
Subtract "48" from each side of the equation;
2x + 48 − 48 = 0 − 48 ;
to get:
2x = -48 ;
Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" ;
2x / 2 = -48 / 2 ;
x = -24 ; which is: Answer choice: [C]: "-24" . _________________________________________________________ Method 2) _________________________________________________________
" 2x + 48 = 0 " ; Solve for "x" ;
→ Factor out a "2" in: " 2x + 48" ; and rewrite:
→ " 2(x + 24) = 0 " ;
Divide EACH SIDE of the equation by "2" ;
→ " { [2(x + 24)] / 2 } = { 0 / 2 } ;
→ x + 24 = 0 ;
Subtract "24" from EACH SIDE of the equation; to isolate "x" on one side of the equation; & to solve for "x" ;
→ x + 24 − 24 = 0 − 24 ;
→ x = -24 ; which is: Answer choice: [C]: " -24 " . __________________________________________________________ Method 3) __________________________________________________________
" 2x + 48 = 0 " ; Solve for "x" ;
→ Divide the entire equation (both sides) by "2" ; to simplify :
{2x + 48} / 2 = 0/ 2 ;
to get:
x + 24 = 0 ;
Subtract "24" from EACH SIDE of the equation; to isolate "x" on one side of the equation; & to solve for "x" ;
→ x + 24 − 24 = 0 − 24 ;
→ x = -24 ; which is: Answer choice: [C]: " -24 " . ________________________________________________________
