Đáp án:
$a)$ `x = -1/7`
$b)$ `x = 31/3`
$c)$ `x ∈ {-9; 11}`
$d)$ `x ∈ {1/5; 1/6}`
Giải thích các bước giải:
$a)$ `(6 -2x)/4 = (5 +2x)/3`
`⇔ 4.(5 +2x) = 3.(6 -2x)`
`⇔ 20 +8x = 18 -6x`
`⇔ 8x +6x = 18 -20`
`⇔ 14x = -2`
`⇔ x = -1/7`
Vậy `x = -1/7`
$b)$ `2/3 = (3x +5)/(6x -8)`
`⇔ 2.(6x -8) = 3.(3x +5)`
`⇔ 12x -16 = 9x +15`
`⇔ 12x -9x = 15 +16`
`⇔ 3x = 31`
`⇔ x = 31/3`
Vậy `x = 31/3`
$c)$ `20/(x -1) = (x -1)/5`
$⇔ (x -1).(x -1) = 5.20$
$⇔ (x -1)² = 100$
$⇔ (x -1)² = 10²$
$⇔ \left[ \begin{array}{l}x -1=10\\x -1=-10\end{array} \right. ⇔ \left[ \begin{array}{l}x=11\\x=-9\end{array} \right.$
Vậy `x ∈ {-9; 11}`
$d)$ `(5x -1)(2x -1/3) = 0`
$⇔ \left[ \begin{array}{l}5x -1=0\\2x -\dfrac{1}{3}=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=\dfrac{1}{5}\\x=\dfrac{1}{6}\end{array} \right.$
Vậy `x ∈ {1/5; 1/6}`
