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Mastering One-Step Equations with Opposite Operations

Learn how to isolate variables in one-step equations using the Opposites Rule. This guide provides clear methods for removing terms connected by addition or subtraction by applying the opposite operation on both sides of the equation. Once you've isolated the variable, you'll then solve the equation by multiplying or dividing to find the solution. With step-by-step examples, this resource will help you understand and master the process of solving one-step equations effectively.

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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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