Absolute-value inequalities

Absolute-value inequalities: precalculus practice

Learn to solve absolute-value inequalities by interpreting distance before transforming symbols. Distinguish values inside a tolerance band from values outside an exclusion zone.

The bank includes strict and inclusive endpoints, scaled expressions, negative multipliers and targets, zero-distance exceptions, measurement tolerances and combined bounds. Each worked explanation identifies whether AND or OR is needed and checks boundary behavior.

Prerequisites: absolute-value equations, compound inequalities and interval notation. Questions combine single-select and multiselect formats. For multiselect tasks, assess every statement independently and select the complete correct subset.

The authored practice bank develops from basic interpretation to multistep calculation, applications and error analysis. Delivery order may vary, so every item is self-contained. Solve on paper before comparing the alternatives; then study the worked explanation and try a fresh problem without choices.

Detailed explanations connect the result to its mathematical justification, including domains, endpoints, units or assumptions where relevant. This foundation resource supports college algebra and precalculus preparation. Recognition of a supplied answer remains provisional evidence: written solutions, graph construction where appropriate and a later unfamiliar task provide useful additional checks.