Mastering Linear Equations and Word Problems

From the study guide

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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Practice 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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Flashcard 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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Frequently asked questions

What does the Mastering Linear Equations and Word Problems study guide cover?

It covers the core concepts of Mastering Linear Equations and Word Problems, organized by topic with the key definitions, explanations and takeaways, so it's easier to learn and remember.

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

The practice quiz has 10 multiple-choice questions, each with an explanation. Use it to check what you know and find your gaps.

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How do I study Mastering Linear Equations and Word Problems with flashcards?

There are 10 flashcards on Mastering Linear Equations and Word Problems, with a question on the front and the answer on the back. Try to recall each answer before you flip, and let spaced repetition bring back the ones you miss.

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