Đáp án:
Giải thích các bước giải:
a) |x - 5| = 12
⇔\(\left[ \begin{array}{l}x - 5 = 12\\x - 5 = -12\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x = 12+5\\x = -12+5\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x = 17\\x = -7\end{array} \right.\)
Vậy x ∈ {17;-7}
b) |3x -12| = x+2
⇔\(\left[ \begin{array}{l}3x -12 = x+2\\3x -12 = -(x+2)\end{array} \right.\)
⇔\(\left[ \begin{array}{l}3x -12 = x+2\\3x -12 = -x-2\end{array} \right.\)
⇔\(\left[ \begin{array}{l}3x - x=2+12\\3x +x=-2+12\end{array} \right.\)
⇔\(\left[ \begin{array}{l}2x=14\\4x=10\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=7\\x=5/2\end{array} \right.\)
Vậy x ∈ {7;5/2}
c) |3x + 12| = x+2
⇔\(\left[ \begin{array}{l}3x +12 = x+2\\3x +12 = -(x+2)\end{array} \right.\)
⇔\(\left[ \begin{array}{l}3x +12 = x+2\\3x +12 = -x-2\end{array} \right.\)
⇔\(\left[ \begin{array}{l}3x - x=2-12\\3x +x=-2-12\end{array} \right.\)
⇔\(\left[ \begin{array}{l}2x=-10\\4x=-14\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-5\\x=-7/2\end{array} \right.\) (không thỏa mãn)
Vậy x ∈ ∅
