Question

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

Answer 1

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

Answer 2

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