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Play Video by Math Dude. Section 2-1 Solve one-step Equations S PI 11B: identify the opposite of a rational number SPI 21E: Solve one and two step linear equations. Objectives: Solve one-step linear equations using addition & subtraction. Recall.

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Play Video by Math Dude

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  1. Play Video by Math Dude

  2. Section 2-1 Solve one-step Equations SPI 11B: identify the opposite of a rational number SPI 21E: Solve one and two step linear equations • Objectives: • Solve one-step linear equations using addition & subtraction Recall Opposite of a rational number a number that is the same distance from zero on the number line but in the opposite direction Solution of an equation Values that make an equation true Equivalent equations Equations that have the same solution

  3. Properties of Equality – Used to Solve Equations Addition Property of Equality: For every real number a, b, and c, if a = b, then a + c = b + c. 3 = (2 + 1) 3 + 4 = (2 + 1) + 4 If you add it to one side... then you must ... add it to the other

  4. Use the Addition Property of Equality (APE) Solve the linear equation: x - 4 = 6 x - 4 + 4= 6 + 4 Add 4 to both sides (APE) x = 10 Simplify • Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

  5. Use the Addition Property of Equality (APE) Solve the linear equation: m – 3.24 = 5.2 m – 3.24 + 3.24 = 5.2 + 3.24 Add 3.24 to both sides (APE) m = 16.848 Simplify • Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

  6. Properties of Equality – Used to Solve Equations Subtraction Property of Equality: For every real number a, b, and c, if a = b, then a - c = b – c. 3 = (2 + 1) 3 - 2 = (2 + 1) - 2 If you subtract it from one side... then you must ... subtract it from the other

  7. Use the Subtraction Property of Equality (SPE) Solve the linear equation: x + 4 = 6 x + 4 - 4= 6 - 4 Sub 4 to both sides (SPE) x = 2 Simplify • Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

  8. Use the Subtraction Property of Equality (SPE) Solve the linear equation: p + 4.1 = 5.32 p + 4.1 – 4.1 = 5.32 – 4.1 Sub 4.1 from both sides (SPE) p = 1.22 Simplify • Solve an equation: • isolate a variable on one side of the equal sign and put remaining terms on the other • what you do to one side of the equal sign, you must do to the other

  9. Inverse Operations Inverse Operations: operations that undo one another In the morning…. You go from home to school In the Evening…. You go from school to home Addition undoes Subtraction & Subtraction undoes Addition. Start with 5 and add 3 to get 8 … the inverse would be … Subtract 3 from 8 to go back to 5

  10. Words and Linear Equations Write and solve a linear equation for the following problem. Josh earned $72. Mary and Josh together earned a total of $504. How much money did Mary earn? 1. Define the unknown with a variable. m = Mary’s money 2. Write an equation using the variable to find the amount of money Mary earned. m + 72 = 504 3. Solve the equation using the Subtraction Property of Equality m + 72 – 72 = 504 - 72 m = 432 Mary earned a total of $432.

  11. Real-World and Linear Equations Together, you and your puppy weigh 128 lb. If you alone weigh 115 lb, how much does your puppy weigh? 1. Define the unknown with a variable. p = puppy’s weight 2. Write an equation using the variable to find the puppy’s weight p + 115 = 128 3. Solve the equation using the Subtraction Property of Equality p + 115 – 115 = 128 - 115 p = 13 The puppy weighs about 13 pounds

  12. Check:11 = 6 + aCheck your solution in the original equation. 11 6 + 5Substitute 5 for a. 11 = 11 Geometry and Linear Equations Find the value of a. PQ = PR 11 = 6 + a The lengths of congruent sides are equal. 11 – 6 = 6 + a – 6 Subtract 6 from each side. 5 = a Simplify. The value of a is 5.

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