Solve the inequality. Express your answer using interval notation.
-$$| x + 1 | - 5 \leq 1$$
A) $[ - 7,1 ]$
B) no solution
C) $( - 7,5 )$
D) $[ - 7,5 ]$

Question

Quizplus · Accepted Answer

To solve the inequality $| x + 1 | - 5 \leq 1$, we first isolate the absolute value on one side: $| x + 1 | \leq 6$. This means that the expression inside the absolute value, $x + 1$, must be within 6 units of 0, leading to two inequalities: $x + 1 \leq 6$ and $x + 1 \geq -6$. Solving these gives $x \leq 5$ and $x \geq -7$, respectively, which combined give the interval $[-7, 5]$.

Solve the Inequality ∣x+1∣−5≤1| x + 1 | - 5 \leq 1∣x+1∣−5≤1

Solve the Inequality $| x + 1 | - 5 \leq 1$