Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.
Solve an absolute-value inequality with less than or less than or equal to
Problem
Solve \(|x~-~4|~\le~3\) and express the solution in interval notation.
Big Picture
What this problem is really about
An upper bound on absolute value keeps the variable within a fixed distance of the center, so the solution lies between two boundaries. We’ll rewrite that distance condition as one compound inequality, apply the same shift to all three parts, and preserve the inclusive comparisons. Those inclusion marks then determine whether interval notation uses brackets or parentheses at each end.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
