جواب تمرین صفحه 67 درس 4 ریاضی هشتم (جبر و معادله)

\(\begin{array}{l} - \frac{3}{8}x + 5 = \frac{1}{6}\\\\ \Rightarrow - \frac{3}{8}x = \frac{1}{6} - 5\\\\ \Rightarrow - \frac{3}{8}x = \frac{1}{6} - \frac{{30}}{6} = - \frac{{29}}{6}\\\\ \Rightarrow x = \frac{{ - \frac{{29}}{6}}}{{ - \frac{3}{8}}} = \frac{{29 \times 8}}{{6 \times 3}} = \frac{{29 \times 4}}{{3 \times 3}}\\\\ \Rightarrow x = \frac{{116}}{9}\end{array}\)

\(\begin{array}{l}\frac{5}{{12}}x - \frac{7}{{18}} = 2\\\\ \Rightarrow \frac{5}{{12}}x = 2 + \frac{7}{{18}} = \frac{{36}}{{18}} + \frac{7}{{18}}\\\\ \Rightarrow \frac{5}{{12}}x = \frac{{43}}{{18}}\\\\ \Rightarrow x = \frac{{\frac{{43}}{{18}}}}{{\frac{5}{{12}}}} = \frac{{43 \times 12}}{{18 \times 5}} = \frac{{43 \times 2}}{{3 \times 5}}\\\\ \Rightarrow x = \frac{{86}}{{15}}\end{array}\)

\(\begin{array}{l}4x + \frac{2}{7} = \frac{3}{2}x\\\\ \Rightarrow 4x - \frac{3}{2}x = - \frac{2}{7}\\\\ \Rightarrow \frac{8}{2}x - \frac{3}{2}x = - \frac{2}{7}\\\\ \Rightarrow (\frac{8}{2} - \frac{3}{2})x = - \frac{2}{7}\\\\ \Rightarrow \frac{5}{2}x = - \frac{2}{7}\\\\ \Rightarrow x = \frac{{ - \frac{2}{7}}}{{\frac{5}{2}}} = - \frac{{2 \times 2}}{{7 \times 5}}\\\\ \Rightarrow x = - \frac{4}{{35}}\end{array}\)

\(\begin{array}{l}2x - \frac{2}{3} = 5x + 3\\\\ \Rightarrow 2x - 5x = 3 + \frac{2}{3}\\\\ \Rightarrow (2 - 5)x = \frac{9}{3} + \frac{2}{3}\\\\ \Rightarrow - 3x = \frac{{11}}{3}\\\\ \Rightarrow x = \frac{{\frac{{11}}{3}}}{{ - 3}}\\\\ \Rightarrow x = - \frac{{11}}{9}\end{array}\)

\(\begin{array}{l}1 - \frac{{x + 1}}{2} = \frac{1}{3}\\\\ \Rightarrow 1 - \frac{{x + 1}}{2} - \frac{1}{3} = 0\\\\ \Rightarrow \frac{6}{6} - \frac{{3(x + 1)}}{6} - \frac{2}{6} = 0\\\\ \Rightarrow \frac{{6 - 3(x + 1) - 2}}{6} = 0\\\\ \Rightarrow 6 - 3(x + 1) - 2 = 0\\\\ \Rightarrow 6 - 3x - 3 - 2 = 0\\\\ \Rightarrow - 3x - 1 = 0\\\\ \Rightarrow - 3x = 1\\\\ \Rightarrow x = - \frac{1}{3}\end{array}\)

\(\begin{array}{l}\frac{1}{2} - \frac{{2x - 1}}{4} = \frac{3}{4}\\\\ \Rightarrow \frac{1}{2} - \frac{{2x - 1}}{4} - \frac{3}{4} = 0\\\\ \Rightarrow \frac{2}{4} - \frac{{2x - 1}}{4} - \frac{3}{4} = 0\\\\ \Rightarrow \frac{{2 - (2x - 1) - 3}}{4} = 0\\\\ \Rightarrow 2 - (2x - 1) - 3 = 0\\\\ \Rightarrow 2 - 2x + 1 - 3 = 0\\\\ \Rightarrow - 2x = 0\\\\ \Rightarrow x = 0\end{array}\)

x = طول

\(\begin{array}{l}2(x + 5) = 24\\\\ \Rightarrow 2x + 10 = 24\\\\ \Rightarrow 2x = 24 - 10\\\\ \Rightarrow 2x = 14\\\\ \Rightarrow x = \frac{{14}}{2}\\\\ \Rightarrow x = 7\end{array}\)

\(\begin{array}{l}7x + 4 = 58\\\\ \Rightarrow 7x = 58 - 4\\\\ \Rightarrow 7x = 54\\\\ \Rightarrow x = \frac{{54}}{7}\end{array}\)

n = عدد کوچکتر

\(\begin{array}{l}n\,\,\,,\,\,\,n + 1\,\,\,,\,\,\,n + 2\\\\ \Rightarrow n + (n + 1) + (n + 2) = 27\\\\ \Rightarrow 3n + 3 = 27\\\\ \Rightarrow 3n = 27 - 3\\\\ \Rightarrow 3n = 24\\\\ \Rightarrow n = \frac{{24}}{3}\\\\ \Rightarrow n = 8\end{array}\)

\(\begin{array}{l}5n - 3 = 17\\\\ \Rightarrow 5n = 17 + 3\\\\ \Rightarrow 5n = 20\\\\ \Rightarrow n = \frac{{20}}{5}\\\\ \Rightarrow n = 4\end{array}\)

پاسخ صحیح گزینه د می باشد:

عبارت ریاضی «اگر مربع عددی به آن عدد اضافه شود، عدد حاصل، 42 خواهد بود.» به این صورت می باشد:

\({x^2} + x = 42\)

تنها عددی که از بین گزینه های موجود در این رابطه صدق می کند، عدد 7- می باشد.

\({( - 7)^2} + ( - 7) = 49 - 7 = 42\)

\(\begin{array}{l}(45 + n) = (14 + n) + (9 + n)\\\\ \Rightarrow 45 + n = 23 + 2n\\\\ \Rightarrow 2n - n = 45 - 23\\\\ \Rightarrow n = 22\end{array}\)

\(\left. \begin{array}{l}W = 12\\\\F = 4\end{array} \right\} \Rightarrow 12 = 4d \Rightarrow d = \frac{{12}}{4} \Rightarrow d = 3\)

\(\begin{array}{l}x + 4 = 2x - 3\\\\ \Rightarrow 2x - x = 4 + 3\\\\ \Rightarrow x = 7\end{array}\)

\(\begin{array}{l}2y - {10^ \circ } = 3y - {70^ \circ }\\\\ \Rightarrow 3y - 2y = - {10^ \circ } + {70^ \circ }\\\\ \Rightarrow y = {60^ \circ }\end{array}\)