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nydus/The First Steps in AlgebraPublic

This textbook introduces the fundamental concepts of algebra, including definitions of units, quantities, and number symbols. It explains the use of letters to represent numbers and outlines the signs for basic mathematical operations.

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Table of Contents

II.

  1. x2−2x−3=x2−3x+1.
  1. (x2−9)−(x2−16)+x=10.
  1. x2+8x−(x2−x−2)=5(x+3)+3.
  1. x2+x−2+x2+2x−3=2x2−7x−1.
  1. 10x−(x−5)=2x+47.
  1. 7x−5−(6−8x)+2=3x−7+106.
  1. 6x+3−(3x+2)=(2x−1)+9.
  1. 3(x+10)+4(x+20)+5x−170=15−3x.
  1. 20−x+4(x−1)−(x−2)=30.
  1. 5x+3−(2x−2)+(1−x)=6(9−x).

55. Statement and Solution of Problems.

The difficulties which the beginner usually meets in stating problems will be quickly overcome if he will observe the following directions:

Study the problem until you clearly understand its meaning and just what is required to be found.

Remember that x must not be put for money, length, time, weight, etc., but for the required number of specified units of money, length, time, weight, etc.

Express each statement carefully in algebraic language, and write out in full just what each expression stands for.

Do not attempt to form the equation until all the statements are made in symbols.

We will illustrate by examples:

  1. John has three times as many oranges as James, and they together have 32. How many has each?

lint Let x stand for the number of oranges James has; lintthen 3x is the number of oranges John has; lintand x+3x is the number of oranges they together have.

But 32 is the number of oranges they together have.

x + 3x = 32; lintor, 4x = 32, lintand x = 8. lint Since x=8, 3x = 24.

Therefore James has 8 oranges, and John has 24 oranges.

Beginners in stating the preceding problem generally write: {Letx = {}whatJameshad.}

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