Solve using the addition principle. Don't forget to perform a check. \( x+\frac{1}{8}=-\frac{3}{4} \)

To solve the equation \( x + \frac{1}{8} = -\frac{3}{4} \) using the addition principle, we need to isolate \( x \). To do this, we subtract \( \frac{1}{8} \) from both sides: \[ x = -\frac{3}{4} - \frac{1}{8} \] Next, we need a common denominator to combine the fractions on the right. The least common denominator between 4 and 8 is 8. We convert \( -\frac{3}{4} \) to eighths: \[ -\frac{3}{4} = -\frac{3 \times 2}{4 \times 2} = -\frac{6}{8} \] Now we can combine the fractions: \[ x = -\frac{6}{8} - \frac{1}{8} = -\frac{6 + 1}{8} = -\frac{7}{8} \] Now, let’s perform a check by substituting \( x = -\frac{7}{8} \) back into the original equation: \[ -\frac{7}{8} + \frac{1}{8} = -\frac{6}{8} \] And simplifying: \[ -\frac{6}{8} = -\frac{3}{4} \] Since both sides of the equation are equal, our solution is confirmed: **Final answer: \( x = -\frac{7}{8} \)**. Testing values when solving equations is important; it's like tasting your cake before serving it—make sure it’s just right!