The Life Starter
Sign up
All courses/Life

Course 216 · Life course 38

Solve Equations with Algebra

A checked algebra notebook that models four situations, solves equations and inequalities, and tests solutions against the original conditions. Six introductory lessons use supplied practice cases.

Before you start

Use paper or a free text document; every core input is supplied in the lessons.

Practical Math and Data for Work and Training See everything you’ll need

Free download · Original practice data · No external account required. Download the starter pack

What you’ll leave with

A checked algebra notebook that models four situations, solves equations and inequalities, and tests solutions against the original conditions.

Start course Start without an account. Sign in to save lesson progress across devices.

Your project

Start with the practice files. Build your project one lesson at a time.

Practice files are free without an account. Sign in to save your project record in My Proof: a description, checklist, and optional work link. Keep the original files in your own app or notebook; saving a project record does not upload them.

  1. Get your materialsDownload practice filesSupplied practice cases, a blank working record, complete lesson instructions, and annotated worked examples.
  2. Make your projectView the project checklist Work in your own notebook, document, or software. Use the supplied practice examples when you prefer.
  3. Keep a private recordSave a project record Sign in to save a description and checklist, then return to update them.
Course handbook

Know the route before you begin.

Here’s what you’ll need and what you’ll make. You can return to this guide during any lesson.

Who this is for

Learners aged 14+ building subject foundations and practical independence. Adults can use the same supplied cases.

Prepare before lesson one
  • Use paper or a free text document; every core input is supplied in the lessons.
  • A basic calculator is optional; show the method, units and checks.
  • Suggested earlier course: Practical Math and Data for Work and Training
Your final project

Finish with proof you can use.

A checked algebra notebook that models four situations, solves equations and inequalities, and tests solutions against the original conditions.

Save a project record in My Proof
See project checklist and review criteria

Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.

What to include

  • Include four clearly defined quantity models with units.
  • Show balanced transformations and distribution in at least one model.
  • State a permitted inequality set and check its boundary.
  • Check each final value in its original relationship.
  • Add all six changed-case responses and explain one infeasible whole-number arrangement.

Review and revise

Use these criteria to check your work and choose what to improve.

  • Method: applies the course-specific rules to the supplied cases with visible intermediate work.
  • Accuracy: results agree with the stated facts, units, boundaries and independent checks.
  • Reasoning: explains why the result follows and identifies a limitation or unresolved question.
  • Transfer: completes changed cases and revises the final project when a relevant assumption changes.
Three ideas to help you along the way
Three useful ideas

The rules behind the steps.

01

Name the quantities before calculating

A variable names one quantity whose value is unknown. Write what it measures before writing a relationship. Equal signs state that two expressions have the same value; they do not mean “the next step.”

02

Use the correct relationship

Undo operations in reverse order while preserving equality. Keep each intermediate equation visible, and verify the proposed value in the original equation rather than only in the last line.

03

Keep the check and boundary visible

Model selection starts with the relationship, not the presence of numbers. Distinguish a total equation from a capacity inequality, then check algebraic solutions against the original units and context.

What do these words mean?
Key words

Key terms worth knowing.

Variable
A symbol representing a defined quantity.
Equation
A statement that two expressions have equal values.
Solution
A value satisfying the original statement and context.
Inequality
A comparison describing a set of values.
Coefficient
A number multiplying a variable term.
Your route

6 lessons.
One useful project.

Work in order the first time. Each lesson makes something the next lesson can use.

  1. 1
    Up next

    Represent an unknown with units

    Translate equal groups and a fixed amount into an equation with a defined variable.

  2. 2
    8 min

    Keep equations balanced

    Isolate a variable using the same reversible operation on both sides.

  3. 3
    9 min

    Solve multi-step equations

    Solve a two-operation equation and verify the proposed value in its original form.

  4. 4
    10 min

    Handle brackets and like terms

    Distribute a coefficient across a bracket and combine only like terms.

  5. 5
    11 min

    Solve and interpret an inequality

    Solve a linear inequality and restrict its values to the stated context.

  6. 6
    13 min

    Choose and check a model

    Select equality or inequality from a situation and reject contextually infeasible values.

Use the tools

Tools to help you practice.

See all tools
ZIP · practice files

Solve Equations with Algebra practice files

Supplied practice cases, a blank working record, complete lesson instructions, and annotated worked examples.

Text worksheet

Your course project worksheet

A downloadable text worksheet with each lesson’s working output, space for your answers, and the shared final-project checklist. Save your own copy.

Source transparency

Sources and further study.

Explore the references behind the lessons and take your learning further. Source notes explain access and reuse.

OpenStax: equality properties
Source & access notes · checked 2026-10-01

Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement. Exact topic chapters were opened in web result turn 325view 0–14.

Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.

Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.

OpenStax: linear-equation strategy
Source & access notes · checked 2026-10-01

Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.

Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.

Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.

OpenStax: linear inequalities
Source & access notes · checked 2026-10-01

Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.

Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.

Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.

Ready when you are

Start with the first useful move.

You’ll always know what to do, what to make, and where to go next.

Start lesson one