Solve the following equation

Explanation

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

Solution

To isolate the variable term -y on the right side, we eliminate -0.8 by adding 0.8 to both sides.

• This is the equation to solve.  First, we want to isolate the variable term, -y.
  • -0.2 = -0.8 - y
• Add 0.8 to both sides to isolate -y.
  • -0.2 + 0.8 = 0.8 - y + 0.8
• Do the additions.
  • 0.6 = -y

Since the term -y has an understood coefficient of -1, the equation can be written as 0.6 = -1y.  To isolate y, we can either multiply both sides or divide both sides by -1.  If we choose to divide both sides by -1, we proceed as follows.

• Now we want to isolate the variable y
  • 0.6 = -1y
• On the left side, do the division.  The quotient of a positive and a negative number is negative.  On the right side, simplify: \(\require{cancel} \frac{\cancel{-1}^1y}{\cancel{01}_1} = y\)

The solution is -0.6.  Check this by substituting it into the original equation.