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Write an inequality using absolute value if the answer is given double inequality

-2 is less than x and less than 4

Respuesta :

frika

Answer:

[tex]|x-1|<3[/tex]

Step-by-step explanation:

You are given

[tex]-2<x<4[/tex]

Note that

[tex]\dfrac{-2+4}{2}=\dfrac{2}{2}=1,[/tex]

so, first, subtract 1 from this double inequality:

[tex]-2-1<x-1<4-1\\ \\-3<x-1<3[/tex]

Now, rewrite it using absolute value:

[tex]|x-1|<3[/tex]

Meaning: point x is less than 3 units away from point 1.

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