Question

22. Rezolvati in multimea numerelor intregi ecuatiile:
a) |x-2| - 11=-2|x-2|+4
b) -2|x+3|+4|x+3|=15-5|x+3|-1
c) 3|x+1|+5=|x+1|+11
d) -4|2x - 1| + 2 = - |2x - 1|-7.​

Answer 1

Răspuns:

Explicație pas cu pas:

a) |x-2| - 11=-2|x-2|+4

|x-2| + 2 |x-2| = 11 + 4

3 |x-2| = 15

|x-2| = 15 : 3 = 5

x - 2 = 5

x1 = 5 + 2 = 7

x - 2 = -5

x2 = -5 + 2 = -3

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b) -2|x+3|+4|x+3|=15-5|x+3|-1

-2|x+3| + 4|x+3| + 5|x+3| = 15 - 1

7|x+3| = 14

|x+3| = 14 : 7 = 2

x + 3 = 2

x1 = 2 - 3 = -1

x + 3 = -2

x2 = -2 - 3 = -5

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c) 3|x+1|+5=|x+1|+11

3|x+1| - |x+1| = 11 - 5

2|x+1| = 6

|x+1| = 6 : 2 = 3

x + 1 = 3

x1 = 3 - 1 = 2

x + 1 = -3

x2 = -3 - 1 = -4

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d) -4|2x - 1| + 2 = - |2x - 1|-7

-4|2x - 1| + |2x - 1| = -7 - 2

-3|2x - 1| = -9

|2x - 1| = -9 : (-3) = 3

2x - 1 = 3

2x = 3 + 1 = 4

x1 = 4 : 2 = 2

2x - 1 = -3

2x = -3 + 1  = -2

x = -2 :2 = -1