Mastering Linear Equations and Word Problems

Trecho da ficha de revisão

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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Prévia do quiz

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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Prévia dos flashcards

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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Perguntas frequentes

O que a ficha de revisão sobre Mastering Linear Equations and Word Problems cobre?

A ficha de revisão cobre os conceitos essenciais de Mastering Linear Equations and Word Problems. Está organizada por tópicos para facilitar o aprendizado e a memorização, com definições chave, explicações e resumos.

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Quantas perguntas há no quiz de Mastering Linear Equations and Word Problems?

O quiz contém 10 perguntas de múltipla escolha com correções e explicações detalhadas para cada resposta. Ideal para testar seu conhecimento e identificar lacunas.

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Como estudar Mastering Linear Equations and Word Problems com flashcards?

Revizly oferece 10 flashcards interativos sobre Mastering Linear Equations and Word Problems. Cada cartão apresenta uma pergunta na frente e a resposta no verso, permitindo uma revisão ativa e eficaz baseada na repetição espaçada.

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