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Solving One-Step Equations: Techniques and Applications

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fallon-pittman
18 diapositives · 333 Views · Nov 13, 2014

This guide introduces one-step equations, emphasizing essential vocabulary and concepts. You’ll learn about solutions, equivalent equations, and inverse operations like addition and subtraction, which are crucial for maintaining balance in equations. Through step-by-step examples, discover how to isolate variables effectively. Real-world applications include solving for unknown weights and bank balances. Engage with practice problems to reinforce your understanding and improve your problem-solving skills. Perfect for all students seeking to master basic algebra.

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  1. SOLVING ONE-STEP EQUATIONS

  2. New Vocabulary • Solution: the value of the variable that makes the equation true • Equivalent Equations: equations that have the same solution • Inverse Operations: operations that undo one another, like addition and subtraction

  3. Solving Equations Using Addition and Subtraction Think of the equation like a scale. An equation is like a scale because it shows that two quantities are equal. The scale remains balanced when the same weight is added to both sides. Let’s try some examples! Write down all the steps!

  4. x - 3 + 3 = 8 + 3 x = 11 Add 3 to each side to get the variable alone on one side of the equal sign. Simplify. Example 1: Addition Solve x - 3 = 8.

  5. Example 2: Addition Solve -10 + x = -4. -10 + x = -4 + 10+ 10 x = 6 • Add 10 to each side to isolate the variable on one side of the equal sign. • Simplify.

  6. Example 3: Addition Try this one on your own! Solve x - 2.5 = 6.4. x - 2.5 = 6.4 x = 8.9 • Did you add 2.5 to both sides? • Then did you simplify? + 2.5+2.5

  7. Example 4: Subtraction Solve x + 8 = -2. x + 8 - 8 = -2 - 8 x = -10 • Perform the inverse operation to get x by itself on one side of the equal sign. • Simplify.

  8. Example 5: Subtraction Solve 3 + x = -1. 3 + x = -1 -3 -3 x = -4 • Subtract 3 from both sides to get the variable alone on one side of the equal sign. • Simplify.

  9. Example 6: Subtraction Try this one on your own! Solve x + 3.4 = 7.7. • Did you subtract 3.4 from both sides? • Then did you simplify? x + 3.4 = 7.7 - 3.4 - 3.4 x = 4.3

  10. Think Think Think! Let’s work it out! Real World Problem Solving How much does the backpack weigh? A student puts on his backpack and steps on the scale, which then reads 156 pounds. He steps on the scale alone and it reads 134 pounds. Write and solve an equation to find the weight of the backpack.

  11. Relate: Define: Write: Backpack’s weight plus students weight equals scale reading. Let w = backpack’s weight. w + 134 = 156 Real World Problem Solving

  12. Real World Problem Solving w + 134 = 156 - 134 -134 w = 22 The backpack weighs 22 pounds.

  13. Now you try! Bank Account Balance Kate withdrew $25 from her savings account. The transaction slip said that her balance was then $347.88. Write and solve an algebraic equation to find Kate’s previous balance.

  14. Now you try! • Relate: • Define: • Write: • Previous balance minus withdrawal equals current balance. • Let p = previous balance. • p - 25.00 = $347.88

  15. Now you try! p - 25.00 = $347.88 + 25.00 + 25.00 p = $372.88 Kate’s previous balance was $372.88.

  16. This triangle is isosceles so sides AB and BC are congruent. Find the value of a. AB = BC 16 = a - 3.9 + 3.9 + 3.9 19.9 = a Real World Problem Solving B 16 a - 3.9 C A

  17. Now you try! • This triangle is isosceles so sides XY and YZ are congruent. • Find the value of b. XY = YZ b - 37 = 24 + 37 + 37 b = 61 Y 24 b - 37 X Z

  18. n - 2 = -5 c - 4 = 9 28.32 = p - 32.96 -31 = 26 + a 5.25 + x = 3.75 v - 17 = 23 (-3) (13) (61.28) (-57) (-1.50) (40) Practice Problems Please take a few minutes to complete the following practice problems in your notes.