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# 2.1 solving 1-step equations

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1. 2.1 solving 1-step equations I can solve one-step equations in one variable.

2. Equivalent Equations • Equations that have the same solutions. • In order to solve a one-step equation, you can use the properties of equality and inverse operations

3. Addition and subtraction properties of equality • Adding the same number to each side of an equation produces an equivalent equation. • x – 3 = 2 • x – 3 + 3 = 2 + 3 • Subtracting the same number from each side of an equation produces an equivalent equation. • x + 3 = 2 • x + 3 – 3 = 2 - 3

4. Inverse operations • To solve an equation you must isolate the variable by getting the variable alone on one side of the equation. • You do this by using inverse operations, undoing the operation. • Ex: subtraction is the inverse of addition

5. Example • x + 13 = 27 • You want to isolate the variable • x + 13 - 13 = 27 - 13 • Use inverse operations • x + 0 = 14 • Simplify • x = 14

6. Check your answer • Substitute your answer into the original equation. • 14 + 13 = 27 • 27 = 27 • If both sides are not equal, go back and check your work.

7. You try! • -7 = b -3 • b = -4

8. Multiplication and division properties of equality • Multiplying or dividing each side of an equation by the same nonzero number produces an equivalent equation. • a ∙ c = b ∙ c

9. Examples • x = 6 • 5x = 20 • x = 4

10. Solving using reciprocals • What is the solution of • Multiply by the reciprocal on each side • m = 35

11. Assignment • ODDS ONLY • Pg. 85 #11-17, 27,29, 39,41, 43-51, 71