Question

ayudenme con estas desigualdades con valor absoluto
|x|=5
|a+1|=5
|3x-4|<2
|2m-7|>2
|7w+9|<14
|y-3|<9​

Answer 1

Respuesta:

x = {-5;5}

a = {4;-6}

1 < x < 3

5/2 < m < 9/2

-23/7 < w < 5/7

-6 < y < 12

Explicación paso a paso:

|x|=5

x1 = - 5

x2 = 5

x = {-5;5}

|a+1|=5

a + 1 = 5  o  a + 1 = -5

a1 = 5 - 1 = 4  

a2 = -5 - 1 = -6     a = {4;-6}

|3x-4|<2

-2 < 2x - 4 < 2

-2 + 4 < 2x < 2 + 4

2 < 2x < 6

2/2 < x < 6/2

1 < x < 3

|2m-7|>2

-2 < 2m - 7 < 2

-2 + 7 < 2m < 2 + 7

5 < 2m < 9

5/2 < m < 9/2

|7w+9|<14

-14 < 7w+9 < 14

-14 - 9 < 7w < 14 - 9

-23 < 7w < 5

-23/7 < w < 5/7

|y-3|<9​

-9 < y-3 < 9

-9 + 3 < y < 9 + 3

-6 < y < 12