1. The problem is to evaluate the expression $\frac{1}{9} \times 6$ and solve the equation $| -10 + 4 | = -6$. 2. First, calculate $\frac{1}{9} \times 6$. Multiplying a fraction by a whole number means multiplying the numerator by the whole number and keeping the denominator the same: $$\frac{1}{9} \times 6 = \frac{1 \times 6}{9} = \frac{6}{9}$$ 3. Simplify the fraction $\frac{6}{9}$ by dividing numerator and denominator by their greatest common divisor, which is 3: $$\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}$$ 4. Now, consider the equation $| -10 + 4 | = -6$. The absolute value $|x|$ is always non-negative, meaning it cannot be less than zero. 5. Calculate inside the absolute value: $$-10 + 4 = -6$$ 6. So the equation becomes: $$| -6 | = -6$$ 7. The absolute value of $-6$ is $6$, so: $$6 = -6$$ 8. This is false because $6$ does not equal $-6$. Therefore, the equation has no solution. **Final answers:** - $\frac{1}{9} \times 6 = \frac{2}{3}$ - The equation $| -10 + 4 | = -6$ has no solution because absolute values cannot be negative.