Решите уравнение:
1) |x| − 8 = −5;
2) |x| + 5 = 2;
3) |x + 12| = 3;
4) |8 − 0,2x| = 12;
5) |10x − 7| − 32 = −16;
6) ||x| − 2| = 2.
|x| − 8 = −5
x > 0:
x − 8 = −5
x = −5 + 8
x = 3;
x < 0:
−x − 8 = −5
−x = −5 + 8
−x = 3
x = −3.
|x| + 5 = 2
x > 0:
x + 5 = 2
x = 2 − 5
x = −3;
x < 0:
−x + 5 = 2
−x = 2 − 5
−x = −3
x = 3.
|x + 12| = 3
x + 12 > 0:
x + 12 = 3
x = 3 − 12
x = −9;
x + 12 < 0:
−x − 12 = 3
−x = 3 + 12
−x = 15
x = −15.
|8 − 0,2x| = 12
8 − 0,2x > 0:
8 − 0,2x = 12
−0,2x = 12 − 8
x = 4 : −0,2
x = −20
8 − 0,2x < 0:
−8 + 0,2x = 12
0,2x = 12 + 8
x = 20 : 0,2
x = 100.
|10x − 7| − 32 = −16
10x − 7 > 0:
10x − 7 − 32 = −16
10x = −16 + 7 + 32
10x = 23
x = 23 : 10
x = 2,3
10x − 7 < 0:
−10x + 7 − 32 = −16
−10x = −16 − 7 + 32
−10x = 9
x = 9 : −10
x = −0,9.
||x| − 2| = 2
||x| − 2| > 0:
|x| − 2 = 2
|x| = 2 + 2
|x| = 4
