Solving One and Two step Equations Sol A.1

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 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

1) Solve r + 16 = -7

r = = -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

Ex. 2) Solve x + 2 = -3

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 x = = -3 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 = m + 17 = 3 5. b – (-4) = 9

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 = = -x 10.

8. -6m = 48

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

Example 12

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:

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