Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12? x = –2, x = –4 x = –2, x = 4 x = 2, x = –4 x = 2, x = 4
Accepted Solution
A:
The correct answer is: [C]: " x = 2, x = - 4 " . __________________________________________________________ Explanation: __________________________________________________________ Given the function: " f(x) = –5|x + 1| + 3 " ;
for what values of "x" is: " f(x) = -12 " ? ________________________________________________________ Replace the "f(x)" notation with "-12" ;
-12 = –5|x + 1| + 3 ;
↔ –5|x + 1| + 3 = -12 ;
and solve for "x" ; {the values for "x"} ; ______________________________________ We have: ______________________________________ -5|x + 1| + 3 = -12 ;
Subtract "3" from EACH SIDE of the equation:
-5|x + 1| + 3 − 3 = -12 − 3 ;
to get:
-5|x + 1| = -15
Now, divide EACH SIDE of the equation by "-5" ;
{-5|x + 1| } / -5 = -15 / -5 ;
to get:
|x + 1| = 3 . _____________________________________________ To solve for "x" ; _____________________________________________ We have 2 (two values). Let us set up "Case 1" and "Case 2" scenarios: _____________________________________________ Case 1)
" x + 1 = 3 " ;
Subtract: "1" from each side of the equation;
x + 1 − 1 = 3 − 1 ;
to get:
x = 2 ; {So, we know that our answer is going to be: "Answer choice: [C] or [D]" ; since these are the only answer choices given that contain a solution of "x = 2" . _______________________________________________________ Case 2)
" - (x + 1) = 3 " ;
→ " -1(x + 1) = 3 ;
Divide each side of the equation by "-1" ; as follows:
→ {-1(x + 1) } / -1 = 3 / -1 ;
to get:
→ x + 1 = -3 ;
Subtract "1" from each side of the equation:
→ x + 1 − 1 = -3 − 1
to get:
→ x = - 4 . ________________________________________________________ So: x = 2 and -4 ; which is: Answer choice: [C]: " x = 2, x = - 4 " . ________________________________________________________