Question

Resolver las siguientes ecuaciones con valor absoluto

Answer 1

Answers:

The absolute value of a real number (also called modulus) is a "non-negative value of that number without regard to its sign". This is because absolute values are, in fact, distances.

In other words: An absolute value is a number's distance from zero in the Number line, and are solved in the following way:

a)
`|3x-5|=4`

`3x-5=4`

`3x=4+5`

`x=3`

or

`3x-5=-4`

`3x=-4+5`

`x=(1)/(3)`

The value of
`x` is between
`{(1)/(3),3}`

b)
`|5x-3|=(2)/(3)`

`5x-3=(2)/(3)`

`5x=(2)/(3)+3`

`x=(11)/(15)`

or

`5x-3=-(2)/(3)`

`5x=-(2)/(3)+3`

`x=(7)/(15)`

The value of
`x` is between
`{(7)/(15),(11)/(15)}`

c)
`|(3x-2)/(2)+5|=10`

`(3x-2)/(2)+5=10`

`3x-2=10`

`x=4`

or

`(3x-2)/(2)+5=-10`

`3x-2=-30`

`x=-(28)/(3)`

The value of
`x` is between
`{-(28)/(3),4}`

d)
`|(x+3)/(4)-(1)/(2)|=3`

`|(x+3)/(4)-(1)/(2)|=3`

`(x+3)/(4)-(1)/(2)=3`

`(x+3)/(4)=3+(1)/(2)`

`x+3=14`

`x=11`

or

`(x+3)/(4)-(1)/(2)=-3`

`(x+3)/(4)=-3+(1)/(2)`

`x+3=-10`

`x=-13`

The value of
`x` is between
`{-13,11}`