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## Solving One and Two step Equations

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**Why do we do the same thing to both sides of an equation**d + 12 = -5**Why do we do the same thing to both sides of an equation**• https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same--thing-to-both-sides--simple-equations**r + 16**= -7 Ex. 1) Solve r + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!**1) Solve r + 16 = -7**• Draw “the river” to separate the equation into 2 sides • Subtract 16 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem - 16 -16 r = -23 -23 + 16 = -7**2) Solve x + 2 = -3**- 2 - 2 x = -5 -5 + 2 = -3 • Draw “the river” to separate the equation into 2 sides • Subtract 2 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!**Addition and subtraction Properties of Equality**• Definition: Either adding or subtracting the same number to each side of the equation produces an equivalent equation. Example: X - 9 = 15 How can you check your answers?**Try These: Don’t forget to check your answer**3. r – 2 = 21 4. m + 17 = 3 5. b – (-4) = 9**Multiplication and Division Properties of Equality**Definition: If you multiply or divide each side of the equation by the same nonzero number you produce an equivalent equation. Example 6: Multiplication:**Division:**Example 7. 7m=91**Try These:**8. -6m = 48 9. 14 = -x 10.**Solving Equations using Reciprocals**Rule – When the original number is multiplied by it’s reciprocal the product should equal 1. Example 11: Don’t forget to check your answer**Solving Two Step Equations**Note- When solving two step equations Always Isolate the variable first. (i.e. get rid of anything that is not with your variable.) Example 13:**Solving Two Step Equations**Example 14:**Try These:**15. 16. 17.**Solving Two-Step equations by combining like terms**Example: 18. 7x – 4x = 21 19. 5b – 7b = 4