The Easiest Way to Understand Algebra. Algebra equations with answers and solutions. Sergey D. Skudaev
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Название: The Easiest Way to Understand Algebra. Algebra equations with answers and solutions

Автор: Sergey D. Skudaev

Издательство: Издательские решения

Жанр: Руководства

Серия:

isbn: 9785449091154

isbn:

СКАЧАТЬ an equation where all numbers are represented by letters.

      X – b = c

      Apply the first rule to solve this equation

      X – b + b = c + b

      Since, -b + b = 0, then

      X = c + b.

      To solve the equation X + b = c we can apply the second rule.

      If X + b = c then

      X + b – b = c – b

      X = c – b.

      The next example is X +7 = 15

      then X +7 – 7 = 15 – 7 and X = 8

      Do not proceed until you perform some exercises to become comfortable using the first few rules of equations.

      Practice 1. Solving the equations

      Answers: page 19

      Solutions: page 22

      Solve for X:

      1. X – 5 = 0

      2. X +11 = 3

      3. X – ab = 4

      4. X – Y = Z

      5. X – 2a = c

      6. X +3ab = bc

      7. X + k = 1 + k

      8. X – ab = a – ab

      9. X + c = c – b

      10. X – 2a = a – ab

      11. X + cb = 3cb – c

      12. X – 5 + a = 2a – 5

      13. X +3 – k = 6 – 3k

      14. X – 1 – ab = ab – 1

      15. X – a – b = a – b

      16. X +2a – 3c = 3a – 2c

      You can find the answers in appendix 1. If your answer is wrong try again.

      If you can’t get the right answer read the solution in appendix 2.

      Let’s solve the equation

      4X – 5 = 15

      You can apply the first rule.

      4X – 5 +5 = 15 +5 then 4X = 20.

      How can you find X? You can apply the fourth rule.

      If you divide both sides of an equation by the same numbers, this equation will still be true.

      4X / 4 = 20 / 4, then X = 5.

      To solve equation

      aX – b = c

      Apply the first rule.

      aX – b + b = c + b,

      then aX = c + b

      Now apply the fourth rule.

      If aX = c + b, then aX / a = (c + b) / a

      and X = (c + b) / a

      Do not read any more until you perform some exercises.

      Practice 2. Solving the equations

      Answers: page 19

      Solutions: page 24

      Solve for X:

      1. 2X – 3 = 5

      2. 3X – 5 = 4

      3. 5X +6 = 36

      4. 8X – 5 = 43

      5. 7X – 2 = 19

      6. 4X +8 = 20

      7. 6X – a = 2a

      8. 2X + b = 13b

      9. 7X +3a = a + b

      10. 4X – 2a = 4 +2a

      11. 4X – 3a = a

      12. 3X – 2b = 6 – 14b

      13. 6X – 2a = 24b – 20a

      14. aX – 3a = ab – 2a

      15. 2aX + ab = 2a – ab

      16. 3aX – c = 3ac – 7c

      Answers are in appendix 1.

      Solutions are in appendix 2.

      If you have such an equation to solve:

      X/a – 5 = 6

      Then apply the first rule:

      X/a – 5 +5 = 6 +5

      X/a = 6 +5

      X/a = 11

      Then apply the third rule.

      X/a * a = 11 *a

      X = 11a

      Let’s solve the equation:

      2X – 4b = 2bc

      Apply the first rule:

      2X – 4b +4b = 2bc +4b,

      then 2X = 2bc +4b

      Apply the third rule:

      2X/ 2 = (2bc +4b) / 2

      You should know how to divide a binomial by a monomial.

      If you have forgotten it, you could find the rule by yourself. Can you write

      (2bc+4b) /2 = 2bc/2 +4b/2? Yes, you can.

      Let us check. Suppose, c = 2 and b = 3.

      To divide a binomial by 2, try to divide each monomial by 2

      2*3*2/2 +4*3/2 = 12

      Now try to solve the binomial first and then divide by 2

      (2*3*2 +4*3) /2 then 24/2 = 12

      We got the same answer. It means that

      (a+ b) /2 = a/2 + b/2.

      We СКАЧАТЬ