Algebra guideFormal Sciences

Algebra study guide on one topic: clear rules, step-by-step solved examples and exercises with answers

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Algebra study guide on one topic: clear rules, step-by-step solved examples and exercises with answers

Example result

Example for the Standard package

Study guide: solving linear equations, for students aged 13–14

The one rule

An equation is a balance. Whatever you do to one side, you do to the other, and the balance stays level. The goal is to get x alone on one side.

Worked example 3: the unknown on both sides

Solve 5x − 4 = 2x + 11.

  1. Move the x terms to one side: take 2x from both sides. 5x − 2x − 4 = 11, so 3x − 4 = 11.
  2. Move the numbers to the other side: add 4 to both sides. 3x = 15.
  3. Divide both sides by 3. x = 5.
  4. Check: 5 × 5 − 4 = 21 and 2 × 5 + 11 = 21. Both sides match.

Common mistake

In 3(x + 2) = 18, many students write 3x + 2 = 18. The 3 multiplies everything in the brackets: 3x + 6 = 18, so x = 4.

Exercises 7–10

  1. 4x + 3 = x + 18
  2. 2(x − 5) = 14
  3. 7 − x = 3x − 9
  4. 3(2x + 1) = 4x + 15

Answers: 7. x = 5 · 8. x = 12 · 9. x = 4 · 10. x = 6

Files: PDF and Word. The guide is for learning: we do not do homework or tests to be handed in.

Client: a parent whose daughter gets lost when an equation has brackets or the unknown on both sides. Task: a guide at middle school level that starts from the basics and builds up to those two cases. Standard package: up to 8 pages, 6 worked examples, 20 exercises with answers and a summary sheet. Excerpt below.

The client and all details are made up.

About this service

Algebra goes wrong when one step is skipped: a sign lost when brackets are opened, a term moved without changing its sign, a fraction cancelled where it can't be. This guide takes one topic you choose, such as linear equations, factorising, quadratics, inequalities, systems of equations or functions, and explains it in plain words from what the learner already knows, with every step of the worked examples written out, the usual mistakes and exercises from easy to harder with answers. Tell us the grade or course, the textbook if any and where the learner gets stuck. Graphs are kept simple: a table of values and a description of the shape. The guide is for learning: we do not solve homework, tests or exams to be handed in, and the exercises are new ones made for practice. Check the notation against your course.

What is included

  • What you getA PDF and Word file on your algebra topic: the rule explained in plain words, key terms, worked examples solved line by line, common mistakes and exercises with answers. From Standard, a one-page summary sheet with the rules and formulas of the topic; in Premium, a 20-question self-check test and a separate answer key with short explanations.
  • One rule at a timeEach new step builds on the one before
  • Every line shownBrackets, signs and fractions written out, not skipped
  • Check your answerHow to substitute back and catch a mistake
  • Common mistakesLost minus signs, order of operations, wrong cancelling
  • At your levelFrom first equations to college algebra

How it works

  1. 1
    TopicYou name the algebra topic, the grade and the sticking point
  2. 2
    WritingWe write the explanation, solved examples and exercises
  3. 3
    DeliveryYou get the guide in PDF and Word on the order page
  4. 4
    StudyYou practise with it and ask for changes within your package

What we need from you

The exact algebra topic, the grade or course, the country or curriculum and the textbook if there is one, the notation your class uses, what the learner can already do and where they get stuck, the language, and whether the guide is for self-study, a parent or a class. You may attach a syllabus, a list of topics or a page of class notes as Word or PDF files, up to 3. Please do not send graded homework, tests or exam papers to be solved.

We will ask you:

  • Which algebra topic?
  • For what level?
  • What does the learner already know, and what is hard?
  • Which curriculum or textbook should it follow?
  • Language and how the guide will be used

Compare packages

BasicUp to 4 pages$9StandardUp to 8 pages$17PremiumUp to 15 pages with a test$33
Deadline1 day2 days3 days
Revisions123
Pagesup to 4up to 8up to 15
Worked examples3610
Exercises with answers102035
Summary sheetNoYesYes
Test and answer keyNoNoYes, 20 questions
SubjectAlgebraAlgebraAlgebra
OrderOrderOrder

Payment protection

You pay when you order, but the money is released only for accepted work.

  • Fixed priceThe package price does not change after you pay.
  • The money is reservedWhen you pay, the amount is only reserved. It is released to the service once you accept the work.
  • Checked before deliveryEvery result goes through a quality check before it reaches you, and you see it on the order page before accepting it.
  • Free revisionsAsk for changes within your brief as many times as the package allows.
  • Acceptance after 3 daysIf within 3 days of delivery you neither accept the work nor ask for changes, it is accepted automatically. If you write in the order chat after delivery, the order waits; once we answer, we may start the 3 days again and will say so in the chat.
  • Redo or a full refundIf the result does not match your brief and the revisions did not fix it, or the work takes more than twice its deadline, write in the order chat: we will redo the work or refund the payment in full.
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Questions and answers

Can you solve my algebra homework?

No. The guide teaches the method with new examples and exercises; we do not solve homework, tests or exams to be handed in as your own work.

Will it include graphs?

Where the topic needs them, graphs are given simply, as a table of values and a description of the shape, so the learner can sketch them. For exact drawings, use graph paper or a graphing tool.

Which topics can I pick?

One topic per order, for example linear equations, powers, polynomials, quadratic equations, inequalities, systems of equations or functions. For a whole course, order guides topic by topic.

Will it match my course?

We follow the level, curriculum and textbook you name, but programmes, notation and methods differ, so the learner or a teacher should check the guide against the course.

Can a teacher use it with a class?

Yes. Print it and share it with your learners; in Premium the test and the answer key are separate files, so you can hand out the test alone.

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