Practicing Success
The set of all values of x satisfying the inequations $|x -1|≤5$ and $|x|≤2$, is |
[-4, 6] [-4, -2] [-4, -2] ∪ [2, 6] [2, 6] |
[-4, -2] ∪ [2, 6] |
We have, $|x -1|≤5$ and $|x|≤2$ $⇒-5≤-1≤5$ and $(x≤-2\,or\,x≥2)$ $⇒-4≤-1≤6$ and $(x≤-2\,or\,x≥2)$ $⇒ x∈[-4, 6]$ and $x∈(-∞,-2]∪[2, ∞)$ $⇒ x∈[-4, -2] ∪ [2, 6]$ |