--- title: "Modulus Functions and Modulus Equations" description: "Read the modulus as distance from zero, sketch the V-shaped graph it produces, and solve equations and inequalities that contain one." canonical: https://lightmysky.com/learn/mathematics/modulus-functions-and-modulus-equations-mt__W-aDpT5jz source: https://lightmysky.com/learn/mathematics/modulus-functions-and-modulus-equations-mt__W-aDpT5jz.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Modulus Functions and Modulus Equations Read the modulus as distance from zero, sketch the V-shaped graph it produces, and solve equations and inequalities that contain one. Subject: Mathematics · Area: Algebra · Ages 16 to 17 Page: https://lightmysky.com/learn/mathematics/modulus-functions-and-modulus-equations-mt__W-aDpT5jz ## Ready when they can - Sketch y equals the modulus of a linear expression and mark where the graph turns - Solve a modulus equation by splitting into the two cases and rejecting solutions that fail the original - Solve a modulus inequality and write the answer as an interval or a union of intervals ## Lesson: Taming the modulus Read the bars as stretch from zero. The graph makes a V whose bend sits where the inner line hits zero. For y shaped by x minus 3, the bend lands at (3, 0). **Example.** Split each equation into twin cases, one per sign. For bars round 2x minus 4 set to 6, work 2x minus 4 as 6 and as minus 6. The roots are 5 and minus 1. Each root must face the first equation. Some guests fail at the door, as in bars round x set to x plus 2, where 1 breaks the check and just minus 1 stays. Keep just the ones that pass. **Tip.** Gaps use stretch sense too. Bars round x minus 1 under 4 means within 4 of 1, so minus 3 through 5. Past marks split outward with OR: bars round x minus 2 past 5 means x past 7 or x under minus 3. **Recap.** Split by sign, test each guest in the first equation, and read gaps as near or far. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Transformations of Graphs](https://lightmysky.com/learn/mathematics/transformations-of-graphs-mt_691_c-7Z5M) - [Solving Linear Inequalities and Solution Sets](https://lightmysky.com/learn/mathematics/solving-linear-inequalities-and-solution-sets-mt_QkG3Cw5VgM) - [Absolute value as distance from zero](https://lightmysky.com/learn/mathematics/absolute-value-as-distance-from-zero-mt_RWUY7_IXvw) - [Function Notation and Evaluating Functions](https://lightmysky.com/learn/mathematics/function-notation-and-evaluating-functions-mt_YWKWzHK_6Z) ## Opens up - [Rational Functions, Asymptotes and Curve Sketching](https://lightmysky.com/learn/mathematics/rational-functions-asymptotes-and-curve-sketching-mt_U-f9YTNb2o)