Solve the following equation

Explanation

We will use properties 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 m = a number, whose solution is obvious.

Solution

We note that the coefficient of m is \(\frac58\) and proceed as follows.

• To isolate the variable terms \(\frac58m\), we add 2 to both sides to undo the subtraction of 2.
• To isolate the variable, m, we multiply both sides by \(\frac85\) to undo the multiplication by \(\frac58\)

• This is the equation to solve.  First we want to isolate the variable terms, \(\frac58m\)
  • \(\frac58m - 2 = -12\)
• Use the addition property of equality:  Add 2 to both sides to isolate \(\frac58m\)
  • \(\frac58m -2 + 2 = -12 + 2\)
• Do the additions: -2 + 2 = 0 and -12 + 2 = -10.  Now we want to isolate the variable, m
  • \(\frac85 \left( \frac58m \right) = \frac85 \left( -10 \right) \)
• On the left side: \(\frac85 \left( \frac58 \right) = 1 \) and 1m = m.  On the right side: \(\require{cancel} \frac85 \left(-10 \right) = -\frac{8 \cdot 2 \cdot \cancel{5}^1}{\cancel{5}_1} = -16\)
  • m = -16

The solution is -16. Check by substituting 16 into the original equation.