Solve the following equation

Explanation

We will use a property of equality to isolate the variable on one side of the equation.  To solve the original equation, we want to find a simpler equivalent equation of the form y = a number or a number = y, whose solution is obvious.

Solution

To isolate y on the right side, we use the addition property of equality.  We can undo the subtraction of 7 by adding 7 to both sides.

• This is the equation to solve
  • -19 = y - 7
• Add 7 to both sides
  • -19 + 7 = y - 7 + 7
• On the left side, add.  On the right side, the sum of a number and its opposite is zero: -7 + 7 = 0
  • -12 = y

Check

• This is the original equation
  • -19 = y - 7
• Substitute -12 for y
  • -19 = -12 - 7

-19 = -19 (True)

Since the statement -19 = -19 is true, the solution is -12