Questions: Solve this equation by adding the opposite to both sides. Make sure your answer is fully reduced. x + (-1/6) = 2/3

Solution Steps

To solve the equation \( x + \left(-\frac{1}{6}\right) = \frac{2}{3} \), we need to isolate \( x \) by adding the opposite of \(-\frac{1}{6}\) to both sides. This will eliminate the \(-\frac{1}{6}\) on the left side, leaving \( x \) by itself. Finally, simplify the resulting expression on the right side to find the value of \( x \).

Starting with the equation: \[ x + \left(-\frac{1}{6}\right) = \frac{2}{3} \] we add \(\frac{1}{6}\) to both sides to isolate \( x \): \[ x = \frac{2}{3} + \frac{1}{6} \]

To add the fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. We rewrite \(\frac{2}{3}\) as: \[ \frac{2}{3} = \frac{4}{6} \] Now, we can add the fractions: \[ x = \frac{4}{6} + \frac{1}{6} \]

Adding the fractions gives: \[ x = \frac{4 + 1}{6} = \frac{5}{6} \]

Final Answer