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Solving One and Two step Equations Sol A.1

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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!

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1) Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

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1) Solve r + 16 = -7

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- 16 -16 r = -23 -23 + 16 = -7 1) Solve r + 16 = -7 1.Draw “the river” to separate the equation into 2 sides 2.Subtract 16 from both sides 3.Simplify vertically 4.Check your answer by substituting your answer back into the problem

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Ex. 2) Solve x + 2 = -3

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2) Solve x + 2 = -3 1.Draw “the river” to separate the equation into 2 sides 2.Subtract 2 from both sides 3.Simplify vertically 4.Check your answer by substituting your answer back into the problem - 2 - 2 x = -5 -5 + 2 = -3 On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

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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?

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Try These: Don’t forget to check your answer 3. r – 2 = 21 4. m + 17 = 3 5. b – (-4) = 9

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3. r – 2 = 21

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4. m + 17 = 3

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5. b – (-4) = 9

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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:

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Division: Example 7. 7m=91

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Try These: 8. -6m = 48 9. 14 = -x 10.

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8. -6m = 48

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9. 14 = -x

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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

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Example 12

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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:

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Solving Two Step Equations Example 14:

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Try These: 15. 16. 17.

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15.

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Solving Two-Step equations by combining like terms Example: 18. 7x – 4x = 21 19. 5b – 7b = 4

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