Question

Solve the Question |x-5|=2.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

By the definition of modulus function

$f(x) = |x| = \left \{ {{x ~\text{if} ~ x \geq 0 } \atop {-x ~\text{if}~x < 0 }} \right.$

So,

$|x-5| = \left \{ {{x-5~\text{if}~ x \geq 5} \atop {-(x-5)~\text{if}~x<5}} \right.$

Case-I:

when x≥5,

we have |x-5| = 2

or, x-5 = 2

or,x=7

and x= 7 is a valid solution becuase 7 ≥5

Case-II:

when x<5,

we have |x-5| =2

or, -(x-5) = 2

or, 5-x = 2

or, x =3

and x = 3 is also a valid solution because 3 < 5

Therefore, x=3,7 are the solutions of the equation