1. Problem: Evaluate the expression $7 + | -7 |$. 2. Recall that the absolute value $|x|$ is the distance of $x$ from zero on the number line, so it is always non-negative. 3. Calculate $| -7 | = 7$ because the absolute value of $-7$ is $7$. 4. Substitute back: $7 + | -7 | = 7 + 7$. 5. Add: $7 + 7 = 14$. 1. Problem: Evaluate the expression $| -16 + 8 |$. 2. Simplify inside the absolute value first: $-16 + 8 = -8$. 3. Calculate the absolute value: $| -8 | = 8$. 1. Problem: Evaluate the expression $-24 - | -24 |$. 2. Calculate the absolute value: $| -24 | = 24$. 3. Substitute back: $-24 - 24$. 4. Perform the subtraction: $-24 - 24 = -48$. 1. Problem: Evaluate the expression $| - \frac{4}{25} |$. 2. The absolute value of a fraction is the fraction without the negative sign: $| - \frac{4}{25} | = \frac{4}{25}$. Final answers: 37. $14$ 38. $8$ 39. $-48$ 40. $\frac{4}{25}$