Question

Solve abs(x – 4)+6 = 13.A. x= 11 and x =-3=B. x = 11 and 2 = = -11C. x= -11 and 2 = 3D. x = -11 and x = -3

Answer 1

Solving for x,

$\begin{gathered} \lvert x-4\rvert+6=13\rightarrow\lvert x-4\rvert=7\rightarrow(x-4)^2=7^2 \\ \\ \rightarrow x^2-8x+16=49\rightarrow x^2-8x-33=0\rightarrow(x-11)(x+3)=0 \\ \\ \rightarrow x-11=0\Rightarrow x_1=11 \\ \\ \rightarrow x+3=0\Rightarrow x_2=-3 \end{gathered}$

Therefore, the correct answer is:

A. x= 11 and x = -3