Решите уравнение:
1) |x| + 6 = 13;
2) |x| − 7 = −12;
3) 7|x| − 3 = 0;
4) |x − 5| = 4;
5) |9 + x| = 0;
6) |x − 4| = −2;
7) |3x + 4| = 2;
8) |2x + 1| + 13 = 14;
9) ||x| − 3| = 5.
|x| + 6 = 13
x > 0:
x + 6 = 13
x = 13 − 6
x = 7;
x < 0:
−x + 6 = 13
−x = 13 − 6
x = −7.
|x| − 7 = −12
x > 0:
x − 7 = −12
x = −12 + 7
x = −5;
x < 0:
−x − 7 = −12
−x = −12 + 7
−x = −5
x = 5.
7|x| − 3 = 0
x > 0:
7x − 3 = 0
7x = 3
|x − 5| = 4
x − 5 > 0:
x − 5 = 4
x = 4 + 5
x = 9;
x − 5 < 0:
−x + 5 = 4
−x = 4 − 5
−x = −1
x = 1.
|9 + x| = 0
9 + x > 0:
9 + x = 0
x = 0 − 9
x = −9;
9 + x < 0:
−9 − x = 0
−x = 9
x = −9.
|x − 4| = −2
−2 − модуль не может быть отрицательным, поэтому уравнение не имеет решений.
|3x + 4| = 2
3x + 4 > 0:
3x + 4 = 2
3x = 2 − 4
3x = −2
|2x + 1| + 13 = 14
2x + 1 > 0:
2x + 1 + 13 = 14
2x = 14 − 13 − 1
2x = 0
x = 0;
2x + 1 < 0:
−2x − 1 + 13 = 14
−2x = 14 − 13 + 1
−2x = 2
x = 2 : −2
x = −1
||x| − 3| = 5
|x| − 3 > 0:
|x| − 3 = 5
|x| = 5 + 3
|x| = 8;
