Question

8 which expression is equivalent to \\(\frac{3}{14}x + (-1) + (-4) - \frac{2}{7}x\\)? \\(\boldsymbol{\text{ⓐ}}\\) \\(5\frac{1}{14}x + 5\\) \\(\boldsymbol{\text{ⓑ}}\\) \\(-5\frac{1}{14}x - 5\\) \\(\boldsymbol{\text{ⓒ}}\\) \\(-\frac{1}{14}x - 5\\) \\(\boldsymbol{\text{ⓓ}}\\) \\(\frac{5}{14}x - 5\\)

Explanation:

Step1: Combine like terms for x

First, rewrite \(-\frac{2}{7}x\) with a denominator of 14. \(-\frac{2}{7}x = -\frac{4}{14}x\). Now combine \(\frac{3}{14}x\) and \(-\frac{4}{14}x\):
\(\frac{3}{14}x + (-\frac{4}{14}x) = \frac{3 - 4}{14}x = -\frac{1}{14}x\)

Step2: Combine constant terms

Combine \(-1\) and \(-4\): \(-1 + (-4) = -5\)

Step3: Combine the results

Putting the two parts together, we have \(-\frac{1}{14}x - 5\)

Answer:

C. \(-\frac{1}{14}x - 5\)