||x-1|+2|<=4 PLZ SOLVE THIS QUESTION AND SHOW STEPS (modulus inequality)

Question

||x-1|+2|<=4 PLZ SOLVE THIS QUESTION AND SHOW STEPS (modulus inequality)

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Alexandra 2 months 2021-11-28T15:42:59+00:00 2 Answers 0 views 0

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    0
    2021-11-28T15:44:34+00:00

    Given:

    ||x – 1| + 2| <= 4

    To find:

    PLZ SOLVE THIS QUESTION AND SHOW STEPS

    Solution:

    From given, we have,

    ||x – 1| + 2| ≤ 4

    when we remove mod, we get,

    |x – 1| + 2 ≥ -4       and      |x – 1| + 2 ≤ 4

    |x – 1| ≥ -4 – 2       and      |x – 1| ≤ 4 – 2

    |x – 1| ≥ -6       and      |x – 1| ≤ 2

    Now consider,

    |x – 1| ≥ -6  

    The above condition holds good for all the values of x.

    Now consider,

    |x – 1| ≤ 2

    when we remove mod, we get,

    x – 1  ≥ -2       and      x – 1  ≤ 2

    x ≥ -2 + 1       and      x ≤ 2 + 1

    x ≥ -1       and      x ≤ 3

    So, we have, true for all x, x ≥ -1       and      x ≤ 3

    ∴ The given equation, ||x – 1| + 2| ≤ 4 is true for all the values of x between x ≥ -1  and  x ≤ 3

    0
    2021-11-28T15:44:41+00:00

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