|2−3x|−|6−2x|=5|2-3x|-|6-2x|=5
→|2−3x|=5+|6−2x|→|2-3x|=5+|6-2x|
→2−3x=5+|6−2x|→2-3x=5+|6-2x| hoặc 2−3x=−(5+|6−2x|)=−5−|6−2x|2-3x=-(5+|6-2x|)=-5-|6-2x|
Xét 2−3x=5+|6−2x|2-3x=5+|6-2x|
→|6−2x|=2−3x−5→|6-2x|=2-3x-5
→|6−2x|=−3−3x→|6-2x|=-3-3x ( ĐK −3−3x≥0→x≤−1-3-3x≥0→x≤-1 )
→6−2x=−(−3−3x)=3+3x→6-2x=-(-3-3x)=3+3x hoặc 6−2x=−3−3x6-2x=-3-3x
→6−3=3x+2x→6-3=3x+2x hoặc 6+3=−3x+2x6+3=-3x+2x
→3=5x→3=5x hoặc 9=−x9=-x
→x=53→x=53 (KTMĐK) hoặc x=−9x=-9 (TMĐK)
Xét 2−3x=−5−|6−2x|2-3x=-5-|6-2x|
→|6−2x|=−5−2+3x=3x−7→|6-2x|=-5-2+3x=3x-7 ( ĐK 3x−7≥0→x≥733x-7≥0→x≥7/3 )
→6−2x=3x−7→6-2x=3x-7 hoặc 6−2x=7−3x6-2x=7-3x
→13=5x→13=5x hoặc −1=−x-1=-x
→x=13/5 (TMĐK) hoặc x=1x=1 (KTMĐK)
Vậy x∈{−9;13/5}
câu 2
|2−3x|+5=x−7|2-3x|+5=x-7
⇔|2−3x|=x−12⇔|2-3x|=x-12
TH1: Với x≤23x≤23
2−3x=x−122-3x=x-12
⇔x+3x=2+12⇔x+3x=2+12
⇔4x=14⇔4x=14
⇔x=7/2 (ktmktm)
TH2:Với x >2/3
−2+3x=x−12-2+3x=x-12
⇔3x−x=−12+2⇔3x-x=-12+2
⇔2x=−10⇔2x=-10
⇔x=−5⇔x=-5 (ktmktm)
Vậy x∈∅
a, \(\left|2-3x\right|=x-12\)đk x >= 12
\(\left[{}\begin{matrix}2-3x=x-12\\2-3x=12-x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x=14\\2x=-10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\left(ktm\right)\\x=-5\left(ktm\right)\end{matrix}\right.\)
Vậy pt vô nghiệm
b, Với x < 3
\(3-x+4-x=x+1\Leftrightarrow3x=6\Leftrightarrow x=2\left(tm\right)\)
Với 3 < x < 4
\(x-3+4-x=x+1\Leftrightarrow1=x+1\Leftrightarrow x=0\left(ktm\right)\)
Với x > 4
\(x-3+x-4=x+1\Leftrightarrow x=8\left(tm\right)\)
