BÀI 2 : Tìm x, biết:
a) $\frac{1}{2}$x + $\frac{1}{3}$ = ║-2║
$\frac{1}{2}$x + $\frac{1}{3}$ = 2
$\frac{1}{2}$x = 2 - $\frac{1}{3}$
$\frac{1}{2}$x = $\frac{6}{3}$ - $\frac{1}{3}$
$\frac{1}{2}$x = $\frac{5}{3}$
x = $\frac{5}{3}$ ÷ $\frac{1}{2}$
x = $\frac{5}{3}$ · 2
x = $\frac{10}{3}$
Vậy x = $\frac{10}{3}$
b) $\frac{4·(x-2)}{-5}$ = $\frac{-20}{(x-2)}$
⇒ 4· (x-2) · (x-2) = (-5) · (-20)
4 · (x-2)² = 100
(x-2) ² = 100 ÷ 4
( x-2)² = 25
⇒ \(\left[ \begin{array}{l}x-2=5\\x-2=-5\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=5+2\\x=-5+2\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=7\\x=-3\end{array} \right.\)
Vậy x ∈ { 7; -3}
c) $\frac{11}{2}$ - $\frac{1}{3}$ ║x+1║ = 3$\frac{1}{2}$
$\frac{11}{2}$ - $\frac{1}{3}$ ║x+1║ = $\frac{7}{2}$
$\frac{1}{3}$ ║x+1║ = $\frac{11}{2}$ - $\frac{7}{2}$
$\frac{1}{3}$ ║x+1║ = 2
║x+1║ = 2 ÷ $\frac{1}{3}$
║x+1║ = 2 · 3
║x+1║ = 6
⇒ \(\left[ \begin{array}{l}x+1=6\\x+1=-6\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=6 - 1\\x=-6 - 1\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=5\\x=-7\end{array} \right.\)
Vậy x ∈ { 5 ; -7 }
d) 50% · (x - 2) - 3(1 - $\frac{1}{3}$x ) = -1
0,5 · ( x - 2) - 3 · 1 + 3 · $\frac{1}{3}$x = -1
0,5·x - 0,5 · 2 - 3 + 1 x = -1
0,5·x - 1 - 3 +1 x = -1
0,5·x + 1x = -1 + 1 + 3
x · ( 0,5 + 1) = 3
x · 1,5 = 3
x = 3 ÷ 1,5
x = 2
Vậy x = 2
e) $\frac{4}{5}$x + $\frac{3}{10}$ (x - 5) = $\frac{7}{10}$
$\frac{4}{5}$x + $\frac{3}{10}$x - $\frac{3}{10}$ · 5 = $\frac{7}{10}$
($\frac{4}{5}$ + $\frac{3}{10}$) x - $\frac{3}{2}$ = $\frac{7}{10}$
($\frac{8}{10}$ + $\frac{3}{10}$) x = $\frac{7}{10}$ + $\frac{3}{2}$
$\frac{1}{2}$ x = $\frac{7}{10}$ + $\frac{15}{10}$
$\frac{1}{2}$ x = $\frac{11}{5}$
x = $\frac{11}{5}$ ÷ $\frac{1}{2}$
x = $\frac{11}{5}$ · 2
x = $\frac{22}{5}$
Vậy x = $\frac{22}{5}$
f) $\frac{3}{4}$ ( x + $\frac{8}{9}$) - $\frac{1}{6}$ x = 5$\frac{1}{3}$
$\frac{3}{4}$ x + $\frac{3}{4}$ · $\frac{8}{9}$ - $\frac{1}{6}$ x = $\frac{16}{3}$
$\frac{3}{4}$ x + $\frac{2}{3}$ - $\frac{1}{6}$ x = $\frac{16}{3}$
$\frac{3}{4}$ x - $\frac{1}{6}$ x = $\frac{16}{3}$ - $\frac{2}{3}$
( $\frac{3}{4}$ - $\frac{1}{6}$) x = $\frac{14}{3}$
($\frac{9}{12}$ - $\frac{2}{12}$ ) x = $\frac{14}{3}$
$\frac{7}{12}$ x = $\frac{14}{3}$
x = $\frac{14}{3}$ ÷ $\frac{7}{12}$
x = $\frac{14}{3}$ · $\frac{12}{7}$
x = 8
Vậy x = 8
g) 1$\frac{1}{5}$ - ( 3$\frac{1}{2}$ - 0,75x ÷ 2$\frac{1}{4}$ ) = 0
$\frac{6}{5}$ - ( $\frac{7}{2}$ - $\frac{3}{4}$ x ÷ $\frac{9}{4}$) = 0
$\frac{7}{2}$ - $\frac{3}{4}$ x ÷ $\frac{9}{4}$ = $\frac{6}{5}$ - 0
$\frac{7}{2}$ - $\frac{3}{4}$ x ÷ $\frac{9}{4}$ = $\frac{6}{5}$
$\frac{3}{4}$ x ÷ $\frac{9}{4}$ = $\frac{7}{2}$ - $\frac{6}{5}$
$\frac{3}{4}$ x ÷ $\frac{9}{4}$ = $\frac{35}{10}$ - $\frac{12}{10}$
$\frac{3}{4}$ x ÷ $\frac{9}{4}$ = $\frac{23}{10}$
$\frac{3}{4}$ x = $\frac{23}{10}$ · $\frac{9}{4}$
$\frac{3}{4}$ x = $\frac{207}{40}$
x = $\frac{207}{40}$ ÷ $\frac{3}{4}$
x = $\frac{207}{40}$ · $\frac{4}{3}$
x = $\frac{69}{10}$
Vậy x =$\frac{69}{10}$
h) (3$\frac{2}{3}$ x - 38) · $\frac{1}{70}$ = 70%
3$\frac{2}{3}$ x - 38 = 70% ÷ $\frac{1}{70}$
3$\frac{2}{3}$ x - 38 = $\frac{70}{100}$ · 70
$\frac{11}{3}$ x - 38 = 49
$\frac{11}{3}$ x = 49 + 38
$\frac{11}{3}$ x = 87
x = 87 ÷ $\frac{11}{3}$
x = 87 · $\frac{3}{11}$
x = $\frac{261}{11}$
Vậy x = $\frac{261}{11}$
