Mastering Linear Equations and Word Problems

Revision sheet excerpt

Course Outline

  1. Linear equations with fractions
  2. Solving linear equations with variables
  3. Harder challenge linear equation problems
  4. Word problems: perimeter and dimensions
  5. Word problems: cost, tickets, and integers

1. Linear equations with fractions

Key Concepts & Definitions

  • Linear equation : A linear equation is an equation where the variable appears only to the first power and not inside products of variables.
  • Common denominator : A common denominator is a shared multiple used to rewrite fractions so they can be added or subtracted easily.
  • Distributive property : The distributive property lets you multiply a number across terms inside parentheses.

Essential Points

  • Clear fractions by multiplying both sides by the least common denominator of all fractional coefficients.
  • When fractions include expressions like (x-10) or (2x+5), distribute before combining like terms.
  • After clearing denominators, collect x-terms on one side and constants on the other side.
  • Solve by isolating x, then check by substituting into the original fractional equation.

Memory Hook

Fractions first: clear denominators, then collect x, then isolate x.

2. Solving linear equations with variables

Key Concepts & Definitions

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Quiz preview

1. Why is it useful to combine like terms before solving an equation such as ax+b=cx+d?

2. If a rectangle’s length is 3 cm more than twice its width, which equation models that relationship?

3. Which expression best represents a cost model with a starting fee plus a per-unit rate?

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Flashcards preview

Linear equation — fractions?

Clear denominators before solving.

Solve linear equations — variables?

Isolate the variable on one side.

Hard linear problems — steps?

Distribute, combine, then isolate.

Perimeter problem — formula?

Perimeter = 2(length + width).

Word problem — dimensions?

Translate words into equations for length and width.

Cost word problem — setup?

Express total cost as start + rate×units.

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What does the revision sheet on Mastering Linear Equations and Word Problems cover?

The revision sheet covers the essential concepts of Mastering Linear Equations and Word Problems. It is organized by topic to facilitate learning and memorization, with key definitions, explanations and summaries.

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How many questions are in the Mastering Linear Equations and Word Problems quiz?

The quiz contains 10 multiple-choice questions with detailed corrections and explanations for each answer. Ideal for testing your knowledge and identifying gaps.

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