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One-Step Equations Using Opposite Operations 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. 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. Variable Mark the variable then leave it alone. Move everything away from the variable. C Variable 1. C + 3 = 5 -3 -3 = 2 2. m - 3 = 5 +3 +3 m = 8 “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 5. X + 2.2 = 9.2 - 2.2 - 2.2 X =7 6. X – (-28) = - 48 X + 28 = - 48 - 28 - 28 X = - 76 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) 7. 9x = 45 9 9 x =5 8. - 4m = - 28 -4 -4 m=7 This reads 9 times x So use the opposite. Divide both sides by 9. k (8) (8) 9. 6 8 Now Divide By -1 - k = 48 -1 -1 k = - 48 (-5) 10. x (-5) 11 5 55 = x 3 m 4 12 11. 36 = 4m 4 4 9 = m 12.(3) 2n (3) 12 3 2n = 36 2 2 n = 18 3 13. 5 x 2 4 (4) -5x = 11 4 (4) -20x = 11 -20 -20 -11 X = 20 First, change this to an improper fraction. (5) 14. 50 3(5) y 5 -250 = -3y -3 -3 83.333 = y 1 83 3 = y 6.4 0.8x 4 2 x 9 5 35