Question

a43 - simplify like terms and th
score: 7/13 answered: 7/13
question 8
simplify completely:
\\(\frac{2}{7}x - \frac{8}{5}x - \frac{5}{2}x + \frac{3}{2} - 1 - 1\\)
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Explanation:

Step1: Combine x - terms

Find a common denominator for the coefficients of \(x\). The denominators are 7, 5, and 2. The least common multiple of 7, 5, and 2 is 70.
\[

$$\begin{align*} \frac{2}{7}x - \frac{8}{5}x - \frac{5}{2}x&=\frac{2\times10}{7\times10}x - \frac{8\times14}{5\times14}x - \frac{5\times35}{2\times35}x\\ &=\frac{20}{70}x - \frac{112}{70}x - \frac{175}{70}x\\ &=\frac{20 - 112 - 175}{70}x\\ &=\frac{20 - 287}{70}x\\ &=\frac{-267}{70}x \end{align*}$$

\]

Step2: Combine constant terms

\[

$$\begin{align*} \frac{3}{2}-1 - 1&=\frac{3}{2}-2\\ &=\frac{3}{2}-\frac{4}{2}\\ &=\frac{3 - 4}{2}\\ &=-\frac{1}{2} \end{align*}$$

\]

Step3: Combine results

Put the combined \(x\) - terms and constant terms together.
The simplified expression is \(\frac{-267}{70}x-\frac{1}{2}\)

Answer:

\(\boldsymbol{-\frac{267}{70}x - \frac{1}{2}}\)