Solve the following equation

$\frac{13}{8}$

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, whose solution is obvious. 

To isolate x, we use the subtraction property of equality.  We can undo the addition of \(\frac18\) by subtracting \(\frac18\) from both sides

• This is the equation to solve
  • \(x + \frac18 = \frac74\)
• Subtract \(\frac18\)  from both sides
  • \(x + \frac18 - \frac18 = \frac74 - \frac18\)
• On the left side, \(\frac18 - \frac18 = 0\)
  • \(x = \frac74 - \frac18\)
• On the right side, build \(\frac74\) so that it has a denominator of 8
  • \(x = \frac74 \cdot \frac22 - \frac18\)
• Multiply the numerators and multiply the denominators
  • \(x = \frac{14}{8} - \frac18\)
• Subtract the numerators.  Write the result over the common denominator 8
  • \(x = \frac{13}{8}\)

The solution is \(\frac{13}{8}\).  Check by substituting it for x in the original equation.