The document discusses equations and how to solve them. It defines an equation as a mathematical statement indicating two expressions are equal. There are two types: numerical equations with numbers and algebraic equations with variables. The goal in solving equations is to find the value of the variable by rewriting the equation in progressively simpler equivalent forms until the variable is isolated on one side. To do this, the same operation must be applied to both sides of the equation so equivalence is maintained.

1. EquationsIts all about equivalence

2. An equation ….Is a mathematical sentence that says that two expressions are equal.What is on the left = what is on the right

3. There are two types of equations ….. Numerical5 + 9 = 14Algebraic2x – 3 = 14

4. Modeling of equations2x + 4 = -6

5. Model these in your notes:-3x + 4 = 2x5+ 2x = -1 6x – 3 = -2x + 4

6. Our goal with equations is to:Find the value of “x” or the variableSolve itTo do this we must rewrite the equation in progressively simpler equivalent forms of the original equation.

7. So to do this we need to use the most important rule for equations …..What you do to one side you MUST do to the other

8. 2x + 4 = -6From the equation we can choose to try the following:+ 2x -2x

9. 2x + 4 = -6From the equation we can choose to try the following:+ 2x -2x + 4 -4

10. 2x + 4 = -6From the equation we can choose to try the following:+ 2x -2x + 4 -4 -6 + 6

11. 2x + 4 = -6From the equation we can choose to try the following:+ 2x -2x + 4 -4 -6 + 6 x 2 or ÷2

12. 2x + 4 = -6

13. + 2x to both sides4x + 4 = 2x - 6

14. - 2x on both sides4=-2x-6

15. + 4 on both sides2x + 8 = -2

16. -4 on both sides2x = -10

17. -6 on both sides2X – 2 = -12

18. +6 on both sides2x + 10 = 0

19. Multiply both sides by 24x + 8 = -12

20. Divide both sides by 2

21. Divide both sides by 2x + 2 = -3

22. None of these steps are WRONG … an equivalent equation results every timeBUTthe ONE operation that makes the equation simpler (shorter) is the one you are looking for!

23. For these, list all the possible things you could do to each side-3x + 4 = x5+ 2x = -1 5x – 3 = -2x + 4

24. -3x + 4 = x-3x + 3x+ 4 -4+x -xx -3 ÷ -3

25. 5+ 2x = -1 + 5 -5+ 2x -2x-1 +1x 2 ÷ 2

26. 5x – 3 = -2x + 4+ 5x -5x-3 +3-2x +2x+ 4 -4x 5 ÷ 5x -2 ÷ -2

27. For the each of the 3 equations:Write out the equivalent form for each