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Mastering One-Step Equations with Opposite Operations

In this guide, we explore how to isolate variables in one-step equations using the Opposite Operations Rule. To solve equations, it's essential to perform the opposite operation of the term connected to the variable, whether it’s addition or subtraction. This approach is crucial for isolating the variable before solving. Whether dealing with addition or multiplication, clarifying how to use opposite operations will significantly enhance your problem-solving skills in algebra. Practice various examples to become proficient in this fundamental math concept.

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Mastering One-Step Equations with Opposite Operations

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  1. One-Step Equations Using Opposite Operations

  2. When working to get the variable isolated and all alone, use the opposites rule. Opposites Rule – to get rid of a term from either side of an equation, just do the opposite operation.

  3. To ISOLATE a variable, simply add or subtract to get the variable all alone. To get rid of a term that is…….. …connected to its side by addition, subtract it from both sides. To get rid of a term that is…….. …connected to its side by subtraction, add it to both sides.

  4. Variable Mark the variable then leave it alone. Move everything away from the variable. Variable 1. C + 3 = 5 - 3 - 3 2 = C 2. m - 3 = 5 +3 +3 8 m =

  5. “fix” double signs first 3. P + (-12) = -5 P – 12 = -5 +12 +12 P = 7 “fix” double signs first 4. Y - (-6) = 3 Y + 6 = 3 - 6 -6 Y = -3

  6. 5. X + 2.2 = 9.2 - 2.2 - 2.2 X = 7 6. X – (-28) = - 48 X + 28 = - 48 - 28 - 28 = - 76 X

  7. Once you have isolated the variable, you are ready to SOLVE. Multiply or Divide to solve for the variable. To get rid of a term that is……… … connected by multiplication, divide both sides by the number in front of the variable. … connected by division, multiply both sides by the number in front of the variable. (the denominator)

  8. This reads 9 times x So use the opposite. Divide both sides by 9. 7. 9x = 45 9 9 x = 5 8. - 4m = - 28 - 4 - 4 m = 7

  9. This is a division Problem, use Multiplication to solve it. (8) (8) 9. - k = 48 Now Divide By -1 - 1 - 1 k = - 48 (-5) (-5) 10. 55 = x

  10. This is a division problem, Multiply to solve it. Actually cross-multiply. 11. = 4m 36 4 4 = m 9 (3) (3) 12. 36 2n = 2 2 n = 18

  11. + First, change this to an improper fraction. 13. x (5) (5) 14. (4) (4) -5x = -3y -250 = -3 -3 11 -20x = -20 -20 83.333 = y -11 X = = y 20

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