Tìm x , biết: (a) 4/5 x + 5 /6 = 41 /30 ;

15/17

(1,5 điểm) Tìm \(x\), biết:

(a) \(\frac{4}{5}x + \frac{5}{6} = \frac{{41}}{{30}}\);

(b) \(\left| {2x + \frac{4}{3}} \right| = {\left( {0,45} \right)^{2023}}:{\left( {0,45} \right)^{2022}}\);

Nhập câu trả lời ở đây

0/3000 ký tự

Giải thích

a) \(\frac{4}{5}x + \frac{5}{6} = \frac{{41}}{{30}}\)

\(\frac{4}{5}x = \frac{{41}}{{30}} - \frac{5}{6}\)

\(\frac{4}{5}x = \frac{8}{{15}}\)

\(x = \frac{2}{3}\)

Vậy \(x = \frac{2}{3}\).

b) \(\left| {2x + \frac{4}{3}} \right| = {\left( {0,45} \right)^{2023}}:{\left( {0,45} \right)^{2022}}\)

\(\left| {2x + \frac{4}{3}} \right| = {\left( {0,45} \right)^1}\)

\(\left| {2x + \frac{4}{3}} \right| = \frac{3}{{20}}\)

TH1: \(2x + \frac{4}{3} = \frac{3}{{20}}\)

\(2x = \frac{3}{{20}} - \frac{4}{3}\)

\(2x = \frac{{ - 71}}{{60}}\)

\(x = \frac{{ - 71}}{{120}}\).

Vậy \(x = \frac{{ - 71}}{{120}}\).

TH2: \(2x + \frac{4}{3} = \frac{{ - 3}}{{20}}\)

\(2x = \frac{{ - 3}}{{20}} - \frac{4}{3}\)

\(2x = \frac{{ - 89}}{{60}}\)

\(x = \frac{{ - 89}}{{120}}\).

Vậy \(x \in \left\{ {\frac{{ - 71}}{{120}};\,\,\frac{{ - 89}}{{120}}} \right\}\).

c) \(5 + \sqrt x = \frac{5}{2} + \frac{{27}}{8}\)

\(5 + \sqrt x = \frac{{47}}{8}\)

\(\sqrt x = \frac{{47}}{8} - 5\)

\(\sqrt x = \frac{7}{8}\)

\(x = \frac{{49}}{{64}}\).

Vậy \(x = \frac{{49}}{{64}}\).