Problem preview
A-REI.3.1 Warmup M1-010-A11-V01

Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.

Determine endpoint inclusion in an absolute-value graph

Problem

For \(|x-4|\le~3\), identify endpoints, inclusion, marker type, and shaded section.

Big Picture

What this problem is really about

An absolute-value inequality describes distances from a center, so its graph begins with two boundary points equally far from that center. We’ll move the stated distance left and right to locate them, use the equality bar to determine the endpoint markers, and interpret the at-most comparison as the region between the boundaries. A center-point check confirms the intended shaded section.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
A-REI.3.1
Category
Algebra
Domain
Reasoning with Equations and Inequalities
Objective
Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.
Problem type
Determine endpoint inclusion in an absolute-value graph