Answer: Choice (E) x < 1 or x > 7
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Explanation:
Rule: if |x| > k, then x < -k or x > k
Using that rule for the given inequality means we have these steps
|x-4| > 3
x-4 < -3 or x-4 > 3
x < -3+4 or x > 3+4
x < 1 or x > 7 ..... choice E
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Here's a visual way to see why this is the case.
|x-4| represents the distance from x to 4 on the number line.
When we say |x-4| > 3, we want to know which points are more than 3 units away from 4 on the number line.
We can plot 4 on the number line, and then measure 3 units below it (to get to 1) and then 3 units above it (to get to 7). If we're in the region 1 < x < 7, then we're within 3 units of 4 on the number line. Otherwise, we're more than 3 units away from the target we're after.
