Problem preview

A-REI.3.1 Warmup M1-010-A07-V04

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

Decide whether an absolute-value equation with a negative target is possible

Problem

For \(|x-1|\le~-2\), identify right-side sign, possible yes/no, and solution-set classification.

Answer choices

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right side = negative; possible = yes; solution set = -1

right side = negative; possible = no; solution set = empty

right side = nonnegative; possible = yes; solution set = [-1,3]

right side = negative; possible = yes; solution set = all real numbers

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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: Decide whether an absolute-value equation with a negative target is possible