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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

ALGEBRAIC NOTATION.

  1. If James is x years old to-day, how old was he three years ago? How old will he be seven years hence?
  1. Write four times the expression seven minus five. 4(75).
  1. Write seven times the expression 2x minus y.
  1. Write the next integral number above four. 4+1.
  1. If x is an integral number, write the next integral number above it; the next integral number below it.
  1. What number is less than 20 by d?
  1. If the difference of two numbers is five, and the smaller number is fifteen, what is the greater number? 15+5.
  1. If the difference of two numbers is eight, and the smaller number is x, what is the greater number?
  1. If the sum of two numbers is 30, and one of them is 20, what is the other? 3020.
  1. If the sum of two numbers is x, and one of them is 10, what is the other?
  1. If 100 contains x ten times, what is the value of x?

Exercise 7.

  1. In x years a man will be 40 years old; what is his present age?
  1. How old will a man be in y years, if his present age is a years?
  1. What is the value of x if 7x equals 28?
  1. If it takes 3 men 4 days to reap a field, how many days will it take one man to reap it? 3×4.
  1. If it takes a men b days to reap a field, how many days will it take one man to reap it?
  1. What is the excess of 5x over 3x?
  1. By how much does 203 exceed (10+1)? 203(10+1).
  1. By how much does 2x3 exceed (x+1)?
  1. If x stands for 10, find the value of 4(3x20).
  1. If a stands for 10, and b for 2, find the value of 2(a2b).
  1. How many cents in a dollars, b quarters, and c dimes?
  1. A book-shelf contains French, Latin, and Greek books. There are 100 books in all, and there are x Latin and y Greek books. How many French books are there?
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