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- 1. One-Step Equations Vocabulary Equation – a mathematical sentence that contains an equal sign. The equation acts like a balance scale. Solution – a number that can replace a variable in an equation and make a true statement. Algebra- A branch of
- 2. Since an equation is like a balance scale, if you do something to one side, then you have to do it to the other side.
- 3. We solve one-step equations by performing the opposite operation or “inverse operation.” Addition Subtractio n Multiplicatio n Division Subtractio n Addition Division Multiplication
- 4. Inverse operations- two operations that have the opposite effect Addition Subtraction Multiplication Division
- 5. Let’s look at it using algebra Step 1: Complete the inverse operation to both sides of the equation. x + 10 = 15 - 10 10 = 5 x Step 2: Write or “bring down” the result.
- 6. Step 3: Check the solution by “substituting” or
- 7. Solving One-Step Addition Equations
- 8. What if the equation were written this way? x+1=7
- 9. Which operation should we choose to solve? x+1=7 Subtraction
- 10. To keep the equation balanced….. ….we must perform the same operation to both sides.
- 11. Since this is addition, we subtract the same number from both sides. X+1=7 -1 -1
- 12. X+1=7 -1 -1 X =6
- 13. Example 1 m + 18 = 34 -18 -18 m = 16 Do the inverse m + 18 = 34 16 + 18 = 34 34 = 34 substitute in m Look for variable Write what m is Solution is correct!
- 14. Example 1 (bar model) m + 18 = 34 m 18 Look for variable Do the inverse What number does m represent? 34 m = 16 Substitute in m 16 18 34 16 + 18 = 34 34 = 34 Solution is correct!
- 15. Solving One-Step Subtraction Equations
- 16. What if the equation were written this way? x–1=8
- 17. Which operation should we choose to solve? x–1=8 Addition
- 18. To keep the equation balanced….. ….we must perform the same operation to both sides.
- 19. Since this is subtraction, we add the same number to both sides. x–1= 8 + 1 +1
- 20. x–1= 8 + 1 +1 =9 X
- 21. Try These... 1. 2. 3. 4. r + 5 = 18 m - 26 = 59 102 = x - 15 a + 39 = 56 r = 13 m = 85 117 = x a = 17
- 22. Solving One-Step Multiplication Equations
- 23. What if the equation were written this way? 2x = 12
- 24. Which operation should we choose to solve? 2x = 12 Division
- 25. To keep the equation balanced….. ….we must perform the same operation to both sides.
- 26. Since this is multiplication, we divide both sides by the same number. 2x = 12 2 2
- 27. 2x = 12 2 2 X =6
- 28. Solving One-Step Division Equations
- 29. What if the equation were written this way? x -2=4
- 30. Which operation should we choose to solve? x -2=4 Multiplication
- 31. To keep the equation balanced….. ….we must perform the same operation to both sides.
- 32. Since this is division, we multiply both sides by the same number. x–2=4 2(x – 2) = 2(4)
- 33. x– 2=4 2(x – 2) = 2(4) X = 8
- 34. A check only takes 3 steps: 1. Write the original equation. 2. Substitute the answer for the variable. 3. Verify that both sides are equal. 2x = 12 2(6) = 12 12 = 12
- 35. Your Turn: Practice Worksheets 1- 4

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