Question

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Answer 1

Модуль всегда положительное число
То есть |-3|=3 ; |-7/12|=7/12

а)) |х|+ 5/12=1
|х|= 1-5/12
|х|=12/12-5/12
|х|=7/12
Х= 7/12; х= -7/12

Проверка
|7/12|+ 5/12= 1
7/12+5/12=1
12/12=1
1=1

|-7/12|+5/12=1
7/12+5/12=1
12/12=1
1=1


Б)) 7/15+|х|=1
|х|=1-7/15
|х|=15/15-7/15
|х|=8/15
Х=8/15; х=-8/15

Проверка
7/15+|8/15|=1
7/15+8/15=1
15/15=1
1=1

7/15+|-8/15|=1
7/15+8/15=1
15/15=1
1=1


В)) |х|-3/4=1/2
|х|=1/2+3/4
|х|= (1•2)/(2•2)+3/4
|х|=2/4+3/4
|х|=5/4= 1 1/4
Х= 1 1/4; х= -1 1/4

Проверка
|1 1/4|-3/4= 1/2
1 1/4- 3/4= 1/2
5/4-3/4=1/2
2/4=1/2
1/2=1/2

|-1 1/4|-3/4=1/2
1 1/4-3/4=1/2
5/4-3/4=1/2
2/4=1/2
1/2=1/2

Г)) 1- |х|=4/17
1-4/17=|х|
|х|=17/17-4/17
|х|= 13/17
Х=13/17; х= -13/17

Проверка
1-|13/17|=4/17
17/17-13/17=4/17
4/17=4/17

1-|-13/17|=4/17
17/17- 13/17=4/17
4/17=4/17

Д)) |х|+ 3/11= 19/22
|х|= 19/22- 3/11
|х|= 19/22- (3•2)/(11•2)
|х|=19/22-6/22
|х|= 13/22
Х=13/22; х=-13/22

Проверка
|13/22|+ 3/11=19/22
13/22+ 6/22=19/22
19/22=19/22

|-13/22|+3/11=19/22
13/22+6/22=19/22
19/22=19/22

Е)) 6/7+|х|=48/49
|х|=48/49- 6/7
|х|=48/49- (6•7)/(7•7)
|х|=48/49- 42/49
|х|= 6/49
Х=6/49; х=-6/49

6/7+|6/49|=48/49
42/49+6/49=48/49
48/49=48/49

Проверка
6/7+|-6/49|=48/49
42/49+6/49=48/49
48/49=48/49