Question

write $-6 \leq x \leq 6$ as an equivalent inequality containing an absolute value. the equivalent inequality containing an absolute value is \square. (type an inequality.)

Explanation:

Step1: Recall the absolute value inequality property

The inequality \( -a \leq x \leq a \) is equivalent to \( |x| \leq a \) for \( a \geq 0 \).

Step2: Identify \( a \) from the given inequality

In the given inequality \( -6 \leq x \leq 6 \), we can see that \( a = 6 \).

Step3: Apply the property

Using the property from Step 1, with \( a = 6 \), the equivalent absolute - value inequality is \( |x| \leq 6 \).

Answer:

\(|x| \leq 6\)