Đáp án: + Giải thích các bước giải:
$1$.
$a$) `{11}/{24} - 5/{41} + {13}/{24} + 0,5 - {36}/{41}`
`= ({11}/{24} + {13}/{24}) - (5/{41} + {36}/{41}) + 0,5`
`= 1 - 1 + 0,5`
`= 0,5 = 1/2`.
$b$) `23 1/4 . 7/5 - 13 1/4 : 5/7`
`= 7/5 . (23 1/4 - 13 1/4)`
`= 7/5 . (23-13)`
`= 7/5 . 10`
`= 14`.
$c$) `(3/4 + 2/3) : {17}/4 - 3/4`
`= {17}/{12} : {17}/4 - 3/4`
`= 1/3 - 3/4`
`= - 5/{12}`.
$d$) `(-5)^2 . 7/{45} + (-5)^2 . {11}/{45}`
`= (-5)^2 . (7/{45} + {11}/{45})`
`= 25. {18}/{45}`
`= 25 . 2/5`
`= 10`.
$2$.
$a$) `3/2 x - 7/3 = - 1/4`
`⇔ 3/2 x = {25}/{12}`
`⇔ x = {25}/{18}`
Vậy `x = {25}/{18}`.
$b$) `3/4 - (x+1/2) = 1/4`
`⇔ x+1/2 = 3/4 - 1/4`
`⇔ x+1/2 = 1/2`
`⇔ x = 1/2 - 1/2`
`⇔ x=0`
Vậy `x=0`.
$c$) `|2x-1| - 1/2 = 1/3`
`⇔ |2x-1| = 1/3 + 1/2`
`⇔ |2x-1| = 5/6`
$⇒$ \(\left[ \begin{array}{l}2x-1=\dfrac{5}{6}\\2x-1=-\dfrac{5}{6}\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}2x=\dfrac{11}{6}\\2x=\dfrac{1}{6}\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x=\dfrac{11}{12}\\x=\dfrac{1}{12}\end{array} \right.\)
Vậy $x$ $∈$ `{1/{12} ; {11}/{12}}`.
