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Solving One-Step Equations Unit 2, Lesson 3 Online Algebra 1 VHS@pwcs

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Reviewing Algebraic Expressions. What operation do these expressions represent? 1. X + 9 2. B – 7 3. 5c 4. 1. Addition 2. Subtraction 3. Multiplication 4. Division It is important to recognize the operation when solving equations. We use inverse operations to solve them.

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Inverse Operations Inverse operations are operations that “undo” each other. For example if you have $100 in your savings account and then you spend $100, you have nothing! Saving and spending “undo” other, so you can look at them as inverses. In math addition undoes subtraction and subtraction undoes addition. They are inverse operations Also multiplication undoes division and division undoes multiplication. Multiplication and division also “undo; each other, so they are also inverse operations.

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Equations All of the following are examples of equations. 3x + 2y = 7 X = -16 -3x – 8 = 19

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Equations What do we know about equations? Equations all have an =, that is what makes them different from expressions. The equal sign divides the equation into 2 sides Both sides of an equation have the same value. Equations are balanced What you do to one side you must do to the other!

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Solving Equations The goal to solving any equation is to get the variable all by itself! That is when we know we are done. We do this by: 1. Determining what number is on the same side of the equation as the variable. If you have trouble seeing this draw a line through the equal sign. 2. Using inverse operations to get rid of that number.

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Addition Equations Solve: x + 9 = -21 x + 9 = -21 - 9 - 9 x = -30 Check - 30 + 9 = -21 -21 = -21 This is true so you are right! 1. What is on the same side as the x? Remember to draw a line if it helps. 2. Subtract the 9 from both sides. 3. X is alone, so you have solved the equation. 4. To check to see if you are right, sub in you answer for x and simplify. If both sides are equal, you are right. If not go back and check your math!

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Try this on your own! 1. What is one the same side as the x? Remember to draw a line if it helps. 2. Add 16 to both sides. 3. X is alone, so you have solved the equation. 4. To check to see if you are right, sub in you answer for x and simplify. If both sides are equal, you are right. If not go back and check your math! x + -16 = 32 16 16 x = 48 Check: 48 + -16 = 32 32 = 32 Remember if this wasn’t true, then you would need to go back and start again!

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Subtraction Equations Always change these to addition equations, using the definition of subtraction we learned in Lesson 1.2, Integers. x – 9 = -12, becomes x + - 9 = -12 v – (-6) = 24 becomes v + 6 = 24 What does -16 = y – 8 become? -16 = y + - 8

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Subtraction Equations Solve this: g – 45 = 23 g + - 45 = 23 45 g = 68 Check: 68 – 45 = 23 23 = 23 1. Change your equation to addition. 2. What is on the same side as the g? Remember to draw a line if it helps. 3. Add 45 to both sides. 4. g is alone, so you have solved the equation. 5. To check to see if you are right, sub in you answer for g and simplify. If both sides are equal, you are right. If not go back and check your math!

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Try these on your own! Click to see the work and answers! -12 = t – (-11) -12 = t + 11 -11 -11 -23 = t Check: -12 = -23 – (-11) -12 = -23 + 11 -12 = -12 b – 18 = -23 b + -18 = -23 18 18 b = -5 Check: -5 – 18 = -23 -5 + -18 = -23 -23 = -23

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Multiplication Equations Multiplication equations can be solved by dividing the number in front of the variable (the coefficient) into both sides. Example: -5x = 45 -5 - 5 x = -9 Check: -5(-9) = 45 45 = 45 -5 is the coefficient in front of x. Divide both sides by – 5 Check, by subbing in your answer for x

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Try these on your own. Click for the steps and answers! 11v = -99 11 11 v = -9 Check 11(-9) = -99 -99 = -99 10c = 158 10 10 c = 15.8 Check: 10(15.8) = 158 158 = 158

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Division Equations Remember that multiplication “undoes” division, so to solve division equations we multiply both sides of the equations by the denominator. b = 72 1.8 is in the denominator, so we multiply both sides of the equation by 8. 2.Check by subbing 72 back into the equation and simplifying. Check:

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Try these on your own. Click for the steps and answers! Check:

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Equation Review Equations all have an =, that is what makes them different from expressions. The equal sign divides the equation into 2 sides Both sides of an equation have the same value. Equations are balanced What you do to one side you must do to the other!

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