1 Which expression ifequivalent to \( 10 k+17-7 j=10-11 k ? \) \( 0-8, k=1 \) \( 0-7 j=k-1 \) \( 0-7 j+k+1 \) \( 0-8 j-k \)

Solve the equation by following steps: - step0: Solve for \(j\): \(10k+17-7j=10-11k\) - step1: Move the expression to the right side: \(-7j=10-11k-\left(10k+17\right)\) - step2: Subtract the terms: \(-7j=-7-21k\) - step3: Change the signs: \(7j=7+21k\) - step4: Divide both sides: \(\frac{7j}{7}=\frac{7+21k}{7}\) - step5: Divide the numbers: \(j=1+3k\) To find an expression equivalent to \( 10k + 17 - 7j = 10 - 11k \), we first solve for \( j \). 1. Rearranging the equation: \[ 10k + 17 - 7j = 10 - 11k \] 2. Move all terms involving \( j \) to one side and the rest to the other side: \[ -7j = 10 - 11k - 10k - 17 \] Simplifying the right side: \[ -7j = -21k - 7 \] 3. Dividing both sides by -7: \[ j = 3k + 1 \] Now, we can express \( j \) in terms of \( k \) as \( j = 3k + 1 \). Next, we will check which of the given expressions is equivalent to this result: 1. **Expression 1:** \( 0 - 8, k = 1 \) - This does not relate to \( j \). 2. **Expression 2:** \( 0 - 7j = k - 1 \) - Rearranging gives \( 7j = 1 - k \), or \( j = \frac{1 - k}{7} \), which is not equivalent. 3. **Expression 3:** \( 0 - 7j + k + 1 \) - Rearranging gives \( 7j = k + 1 \), or \( j = \frac{k + 1}{7} \), which is not equivalent. 4. **Expression 4:** \( 0 - 8j - k \) - Rearranging gives \( 8j = -k \), or \( j = -\frac{k}{8} \), which is not equivalent. None of the provided expressions are equivalent to \( j = 3k + 1 \). Thus, the answer is that none of the expressions are equivalent to the original equation.