How do you solve $| a + 1 | \leq 4$ $|a+1|\le 4$ ?

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Answer 1 · 2018-06-08T07:58:58

$- 5 \leq a \leq 3$ $-5\le a\le 3$

By definition, $| x | \leq k \Leftrightarrow - k \leq x \leq k$ $|x|\le k \iff -k \le x \le k$

So, $| a + 1 | \leq 4 \Leftrightarrow - 4 \leq a + 1 \leq 4$ $|a+1|\le 4 \iff -4 \le a+1 \le 4$

Subtract $1$ $1$ from all sides to get

$- 5 \leq a \leq 3$ $-5\le a\le 3$

How do you solve |a+1|\le 4|a+1|≤4|a+1|\le 4?