Explicație pas cu pas:
[tex] |2x - 5| = 11 \\ 2x - 5 = - 11 \\ 2x = - 11 + 5 \\ 2x = - 6 = > x = - 3 \\ 2x - 5 = 11 \\ 2x = 11 + 5 \\ 2x = 16 = > x = 8 \\ \bf x \in \{-3;8\}[/tex]
[tex] |2x + 7| = 13 \\ 2x + 7 = - 13 \\ 2x = - 13 - 7 \\ 2x = - 20 = > x = - 10 \\ 2x + 7 = 13 \\ 2x = 13 - 7 \\ 2x = 6 = > x = 3\\ \bf x \in \{-10;3\}[/tex]
[tex] - 15 + | - 2x - 9| = - 10 \\ | - 2x - 9| = - 10 + 15 \\ | - 2x - 9| = 5 \\ - 2x - 9 = - 5 \\ - 2x = - 5 + 9 \\ - 2x = 4 = > x = - 2 \\ - 2x - 9 = 5 \\ - 2x = 5 + 9 \\ - 2x = 14 = > x = - 7\\ \bf x \in \{-7;-2\}[/tex]
[tex]17 - | - 2x - 5| = 6 \\ | - 2x - 5| = 17 - 6 \\ | - 2x - 5| = 11 \\ - 2x - 5 = - 11 \\ - 2x = - 11 + 5 \\ - 2x = - 6 = > x = 3 \\ - 2x - 5 = 11 \\ - 2x = 11 + 5 \\ - 2x = 16 = > x = - 8 \\ \bf x \in \{-8;3\}[/tex]
[tex] | |x + 4| - 9 | = 6 \\ |x + 4| - 9 = - 6 \\|x + 4| = - 6 + 9 \\ |x + 4| = 3 \\ x + 4 = - 3 \\ x = - 3 - 4 = > x = - 7 \\ x + 4 = 3 \\ x = 3 - 4 = > x = - 1 \\ |x + 4| - 9 = 6 \\ |x + 4| = 6 + 9 \\ |x + 4| = 15 \\ x + 4 = - 15 \\ x = - 15 - 4 = > x = - 19 \\ x + 4 = 15 \\ x = 15 - 4 = > x = 11 \\ \bf x \in \{-19;-7;-1;11\}[/tex]
[tex] | |x + 3| - 6| = 10 \\ |x + 3| - 6 = - 10 \\ |x + 3| = - 10 + 6 \\ |x + 3| = - 4 \ \ nu \ \ exista \ solutii \\ |x + 3| - 6 = 10 \\ |x + 3| = 10 + 6 \\ |x + 3| = 16 \\ x + 3 = - 16 \\ x = - 16 - 3 = > x = - 19 \\ x + 3 = 16 \\ x = 16 - 3 = > x = 13 \\ \bf x \in \{-19;13\}[/tex]
[tex]|9 - |x - 6| | = 13 \\ 9 - |x - 6| = - 13 \\ |x - 6| = 9 + 13 \\ |x - 6| = 22 \\ x - 6 = - 22 \\ x = - 22 + 6 = > x = - 16 \\ x - 6 = 22 \\ x = 22 + 6 = > x = 28 \\ 9 - |x - 6| = 13 \\ |x - 6| = 9 - 13 \\ |x - 6| = - 4 \ \ nu \ \ exista \ solutii \\ \bf x \in \{-16;28\}[/tex]
[tex] |12 - |x - 4| | = 6 \\ 12 - |x - 4| = - 6 \\ |x - 4| = 12 + 6 \\ |x - 4| = 18 \\ x - 4 = - 18 \\ x = - 18 + 4 = > x = - 14 \\ x - 4 = 18 \\ x = 18 + 4 = > x = 22 \\12 - |x - 4| = 6 \\ |x - 4| = 12 - 6 \\ |x - 4| = 6 \\ x - 4 = - 6 \\ x = - 6 + 4 = > x = - 2 \\ x - 6 = 6 \\ x = 6 + 6 = > x = 12 \\ \bf x \in \{-14;-2;12;22\}[/tex]
