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. …connected to its side by subtraction, add it to both sides. To get rid of a term that is……..

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

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

5. X = X= X – (-28) = - 48 X + 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 This reads 9 times x So use the opposite. Divide both sides by x= m = m = 7

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

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

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