Absolute Value Inequalities Quick Check

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Question
Find the solution to −3|x+1|≥−12
. Provide your answer using interval notation.(1 point)
The solution to −3|x+1|≥−12
is [
].
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1 answer

To solve the inequality \(-3|x + 1| \geq -12\), we can start by dividing both sides by \(-3\). Remember that when dividing by a negative number, the direction of the inequality sign changes:

\[ |x + 1| \leq 4 \]

Next, we can rewrite the absolute value inequality \(|x + 1| \leq 4\) as two separate inequalities:

\[ -4 \leq x + 1 \leq 4 \]

Now we can solve for \(x\) by subtracting \(1\) from all parts of the inequality:

\[ -4 - 1 \leq x \leq 4 - 1 \]

This simplifies to:

\[ -5 \leq x \leq 3 \]

In interval notation, this solution is represented as:

\[ [-5, 3] \]

Thus, the solution to \(-3|x+1| \geq -12\) is:

\[ \boxed{[-5, 3]} \]