Tìm x ở các câu sau:

Question

Tìm x

| 2 - 3x | + 5 = x - 7

| x - 3 | + | x - 4 | = x + 1

| 2 - 3x | - | 6 - 2x | = 5

Answer 1

chia thành 3 câu , câu 1 
|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∈∅