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Đáp án + Giải thích các bước giải:

$\text{Bài 1:}$

$\text{a)}$ $\dfrac{1}{4}+$ $\dfrac{3}{4}:x=$ $\dfrac{2}{3}$

$⇔\dfrac{3}{4}:x=$ $\dfrac{2}{3}-$ $\dfrac{1}{4}$

$⇔\dfrac{3}{4}:x=$ $\dfrac{5}{12}$

$⇔x=\dfrac{3}{4}:$ $\dfrac{5}{12}$

$⇔x=\dfrac{9}{5}$

$\text{Vậy ...}$

$\text{b)}$ $(-2)^{x-1}+2007=2263$

$⇔(-2)^{x-1}=2263-2007$

$⇔(-2)^{x-1}=256$

$⇔(-2)^{x-1}=(-2)^{8}$

$⇔x-1=8$

$⇔x=8+1$

$⇔x=9$

$\text{Vậy ...}$

$\text{c)}$ $|\dfrac{1}{2}-x|+$ $\dfrac{1}{3}=$ $2\dfrac{1}{4}$ 

$⇔|\dfrac{1}{2}-x|+$ $\dfrac{1}{3}=$ $\dfrac{9}{4}$ 

$⇔|\dfrac{1}{2}-x|=$ $\dfrac{9}{4}-$ $\dfrac{1}{3}$ 

$⇔|\dfrac{1}{2}-x|=$ $\dfrac{23}{12}$

$⇔\left[\begin{matrix}\dfrac{1}{2}-x=\dfrac{23}{12}\\-(\dfrac{1}{2}-x)=\dfrac{23}{12}\end{matrix}\right.$

$⇔\left[\begin{matrix}\dfrac{1}{2}-x=\dfrac{23}{12}\\-\dfrac{1}{2}+x=\dfrac{23}{12}\end{matrix}\right.$

$⇔\left[\begin{matrix} x=\dfrac{1}{2}-\dfrac{23}{12}\\ x=\dfrac{23}{12}-(-\dfrac{1}{2})\end{matrix}\right.$

$⇔\left[\begin{matrix} x=-\dfrac{17}{12}\\ x=\dfrac{29}{12}\end{matrix}\right.$

$\text{Vậy ...}$

$\text{Bài 2:}$

$\text{a)}$ $\dfrac{x}{7}=$ $\dfrac{y}{5}$ $\text{; x + y = 24}$

$\text{ADTCCDTSBN ta có:}$

$\dfrac{x}{7}=$ $\dfrac{y}{5}=$ $\dfrac{x+y}{7+5}=$ $\dfrac{24}{12}=2$

$+,\dfrac{x}{7}=2⇒x=7.2=14$

$+,\dfrac{y}{5}=2⇒y=2.5=10$

$\text{Vậy ...}$

$\text{b)}$ $\text{4x = 3y và x - y = 25 }$

$\text{Từ 4x = 3y ⇒}$ $\dfrac{x}{3}=$ $\dfrac{y}{4}$

$\text{ADTCCDTSBN ta có:}$

$\dfrac{x}{3}=$ $\dfrac{y}{4}=$ $\dfrac{x-y}{3-4}=$ $\dfrac{25}{-1}=-25$

$+,\dfrac{x}{3}=-25⇒x=-25.3=-75$

$+,\dfrac{y}{4}=-25⇒y=-25.4=-100$

$\text{Vậy ...}$

$\text{#keodang}$