Absolute-value equations

Absolute-value equations: precalculus practice

Understand absolute-value equations through distance and carefully checked cases. Move from simple distances on the number line to equations with variable expressions on both sides.

Practice isolating the absolute value, distinguishing zero and negative targets, solving equal-distance conditions and analyzing sums of distances. Worked solutions track case restrictions and verify candidates in the original equation rather than relying on mechanical branch splitting.

Prerequisites: linear equations, signed arithmetic and elementary inequalities. 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.