Which of the following expressions should be added to \( 7 x \) to get a sum of zero? o \( x^{7} \) \( \frac{1}{7} x \) \( 0 x-7 \)

To find which expression should be added to \( 7x \) to get a sum of zero, we need to set up the equation: \[ 7x + \text{expression} = 0 \] This means that the expression must be the additive inverse of \( 7x \), which is \( -7x \). Now, let's evaluate each of the given expressions: 1. **For \( x^7 \)**: \[ 7x + x^7 \neq 0 \quad \text{(unless } x = 0\text{)} \] 2. **For \( \frac{1}{7} x \)**: \[ 7x + \frac{1}{7} x = 7x + 0.142857x \neq 0 \quad \text{(unless } x = 0\text{)} \] 3. **For \( 0x - 7 \)**: \[ 7x + (0x - 7) = 7x - 7 \neq 0 \quad \text{(unless } x = 1\text{)} \] None of the expressions provided will yield a sum of zero when added to \( 7x \) for all values of \( x \). However, if we consider the expression that would yield zero, it would be \( -7x \). Since none of the options match this, the answer is that none of the provided expressions should be added to \( 7x \) to achieve a sum of zero.