Đáp án+giải thích các bước giải:
a)
$|2x-1|+1=3$
$|2x-1|=2$
TH1:
$2x-1=2$
$2x=3$
$x=\dfrac{3}{2}$
TH2:
$2x-1=-2$
$2x=-1$
$x=\dfrac{-1}{2}$
$\text{Vậy x =}$ $\dfrac{3}{2}$ $\text{hoặc}$ $\dfrac{-1}{2}$
b)
$(\dfrac{1}{2}x-1)^2=\dfrac{9}{16}$
$(\dfrac{1}{2}x-1)^2=(\dfrac{3}{4})^2$
TH1:
$⇒\dfrac{1}{2}x-1=\dfrac{3}{4}$
$⇒\dfrac{1}{2}x=\dfrac{3}{4}+1$
$⇒\dfrac{1}{2}x=\dfrac{7}{4}$
$⇒x=\dfrac{7}{4}:\dfrac{1}{2}$
$⇒x=\dfrac{7}{2}$
TH2:
$⇒\dfrac{1}{2}x-1=\dfrac{-3}{4}$
$⇒\dfrac{1}{2}x=\dfrac{-3}{4}+1$
$⇒\dfrac{1}{2}x=\dfrac{1}{4}$
$⇒x=\dfrac{1}{4}:\dfrac{1}{2}$
$⇒x=\dfrac{1}{2}$
$\text{Vậy x =}$ $\dfrac{7}{2}$ $\text{hoặc}$ $x=\dfrac{1}{2}$
c)
$\text{Áp dụng tính chất dãy tỉ số bằng nhau ta được}$
$\dfrac{x}{7}=\dfrac{y}{3}=\dfrac{x-y}{7-3}=\dfrac{-12}{4}=-3$
$⇒\dfrac{x}{7}=-3⇒x=(-3).7=-21$
$⇒\dfrac{y}{3}=-3⇒y=(-3).3=-9$
$\text{Vậy x= -21; y= -9}$
