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Equations and inequalities: summary and exercises

  • A linear equation is an equation where the power of the variable(letter, e.g. x ) is 1(one). A linear equation has at most one solution
  • A quadratic equation is an equation where the power of the variable is at most 2. A quadratic equation has at most two solutions
  • Exponential equations generally have the unknown variable as the power. The general form of an exponential equation is: k a ( x + p ) = m
  • A linear inequality is similar to a linear equation and has the power of the variable equal to 1. When you divide or multiply both sides of an inequality by any number with a minus sign, the direction of the inequality changes. You can solve linear inequalities using the same methods used for linear equations
  • When two unknown variables need to be solved for, two equations are required and these equations are known as simultaneous equations. There are two ways to solve linear simultaneous equations: graphical solutions and algebraic solutions. To solve graphically you draw the graph of each equation and the solution will be the co-ordinates of the point of intersection. To solve algebraically you solve equation one, for variable one and then substitute that solution into equation two and solve for variable two.
  • Literal equations are equations where you have several letters (variables) and you rearrange the equation to find the solution in terms of one letter (variable)
  • Mathematical modelling is where we take a problem and we write a set of equations that represent the problem mathematically. The solution of the equations then gives the solution to the problem.

End of chapter exercises

  1. What are the roots of the quadratic equation x 2 - 3 x + 2 = 0 ?
  2. What are the solutions to the equation x 2 + x = 6 ?
  3. In the equation y = 2 x 2 - 5 x - 18 , which is a value of x when y = 0 ?
  4. Manuel has 5 more CDs than Pedro has. Bob has twice as many CDs as Manuel has. Altogether the boys have 63 CDs. Find how many CDs each person has.
  5. Seven-eighths of a certain number is 5 more than one-third of the number. Find the number.
  6. A man runs to a telephone and back in 15 minutes. His speed on the way to the telephone is 5 m/s and his speed on the way back is 4 m/s. Find the distance to the telephone.
  7. Solve the inequality and then answer the questions: x 3 - 14 > 14 - x 4
    1. If x ∈ R , write the solution in interval notation.
    2. if x ∈ Z and x < 51 , write the solution as a set of integers.
  8. Solve for a : 1 - a 2 - 2 - a 3 > 1
  9. Solve for x : x - 1 = 42 x
  10. Solve for x and y : 7 x + 3 y = 13 and 2 x - 3 y = - 4

Questions & Answers

what is economics
Julie Reply
what do you mean by means in economics
economic is the wealth of a country.
monetary policy is refer to as being expansionary or contractionary.
important of unemployment
Otwe Reply
Important of unemployed
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what is consumer
Brenda Reply
how do consumer help people
by export trading
How do you mean Jayah
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definition of economics according to Adam Smith
Ijeoma Reply
economic is a wealth of nation
in the view of Adam Smith economics is the study of activities of people in production of wealth
What do you really think is the remedy for scarcity in Nigeria 🇳🇬
John Reply
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zfekere Reply
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importance of economics
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mixed economic
you have just been appointed in the director of finance for your state internal revenue board with the knowledge of elasticity advice the state government on how the I.G.R of the state could be raised through exercise duties bearing in mind the implication and incident of taxing setting products
Kenechukwu Reply
Hello,Thanks for your replay
mention 5 characteristics of traditional societies
Pono Reply
dominance of agriculture and ignorance of development avenues are some characteristics of traditional societies.
what's defined as unemployment
Lyrikal Reply
what is elasticity
Olakunle Reply
Elasticity is defined as the degree of responsiveness of quantity demanded to slight change in price, cost of other products and income of consumer.....
elasticity simply means change. it is the degree of responsiveness of quantity demanded of a commodity to changes in the price of a commodity
what is monetary policy
Monetary Policy; is the objectives of the central bank in exercising its control over money, interest rates, and credit conditions.
So does it mean that ceteris paribus is the same as all other things being equal?
Ghabbie Reply
Yes nothing else has been changed
ways by which trade unoins raise wage of it's members
Ngu Reply
what is economic growth
Victor Reply
increase a amount of goods and services produced as per head of population a period of time
Economic growth and development has been defined in so many ways by various economist. At a time past, people started raising questions about having economic growth as the same in meaning development. They do not mean the same thing but they are however interdependent and inter related.
For economic development is not possible without economic growth but economic growth is possible without economic development. For example, when there is an observed increase in GDP from 3 million to 4 million over a period of 5 years, we say that there is economic growth.
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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