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 x = a number, whose solution is obvious.

Solution

We will use the addition property of equality to isolate x on the left side of the equation.  We can undo the subtraction of 2 by adding 2 to both sides

• This is the equation to solve
  • x - 2 = 3
• Add 2 to both sides
  • x - 2 + 2 = 3 + 2
• On the left side, the sum of a number and its opposite is zero: -2 + 2 = 0.  On the right side, add 3 + 2 = 5.
  • x + 0 = 5
• On the left side, when 0 is added to a number, the result is the same number
  • x = 5

Since 5 is obviously the solution of the equivalent equation x = 5, the solution of the original equation, x - 2 = 3, is also 5.  To check this result, we substitute 5 for x in the original equation and simplify.

• This is the original equation
  • x - 2 = 3
• Substitute 5 for x
  • 5 - 2 = 3
• True
  • 3 = 3

Since the statement 3 = 3 is true, 5 is the solution of x - 2 = 3