Tìm x của biểu thức, biết: a) − 1/ 2 x + 1 /2 = 2/ 3 ; b) 83/ 3 − ( 2x + 1 )^3 = 2/ 3 ;

10/14

(1,75 điểm) Tìm x, biết:

a) \( - \frac{1}{2}x + \frac{1}{2} = \frac{2}{3}\);

b) \(\frac{{83}}{3} - {\left( {2x + 1} \right)^3} = \frac{2}{3}\);

c) \(\frac{1}{4} + \left| {3x - 1\frac{1}{4}} \right| = \frac{3}{2}\).

Nhập câu trả lời ở đây

0/3000 ký tự

Giải thích

a) \( - \frac{1}{2}x + \frac{1}{2} = \frac{2}{3}\)

\( - \frac{1}{2}x = \frac{2}{3} - \frac{1}{2}\)

\( - \frac{1}{2}x = \frac{1}{6}\)

\(x = \frac{1}{6}:\left( { - \frac{1}{2}} \right)\)

\(x = \frac{{ - 1}}{3}\)

Vậy \(x = \frac{{ - 1}}{3}\).

b) \(\frac{{83}}{3} - {\left( {2x + 1} \right)^3} = \frac{2}{3}\)

\({\left( {2x + 1} \right)^3} = \frac{{83}}{3} - \frac{2}{3}\)

\({\left( {2x + 1} \right)^3} = 27\)

Suy ra \(2x + 1 = 3\)

\(2x = 2\)

\(x = 1\)

Vậy \(x = 1\).

c) \(\frac{1}{4} + \left| {3x - 1\frac{1}{4}} \right| = \frac{3}{2}\)

\(\left| {3x - \frac{5}{4}} \right| = \frac{3}{2} - \frac{1}{4}\)

\(\left| {3x - \frac{5}{4}} \right| = \frac{5}{4}\)

Trường hợp 1:

\(3x - \frac{5}{4} = \frac{5}{4}\)

\(3x = \frac{5}{4} + \frac{5}{4}\)

\(3x = \frac{5}{2}\)

\(x = \frac{5}{2}:3\)

\(x = \frac{5}{6}\)

Vậy \(x \in \left\{ {\frac{5}{6};0} \right\}\).

Trường hợp 2:

\(3x - \frac{5}{4} = - \frac{5}{4}\)

\(3x = - \frac{5}{4} + \frac{5}{4}\)

\(3x = 0\)

\(x = 0\)