Tìm x biết
a,|x+5|=100
b,100 – | 25-x | = 40
c,|2x+1| = | 23-x |
d,|11-7x| – | 4x + 3|=0
Tìm x biết a,|x+5|=100 b,100 – | 25-x | = 40 c,|2x+1| = | 23-x | d,|11-7x| – | 4x + 3|=0
By Gabriella
By Gabriella
Tìm x biết
a,|x+5|=100
b,100 – | 25-x | = 40
c,|2x+1| = | 23-x |
d,|11-7x| – | 4x + 3|=0
a. $|x+5|=100$
⇒ \(\left[ \begin{array}{l}x+5=100\\x+5=-100\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=100-5\\x=-100-5\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=95\\x=-105\end{array} \right.\)
b. $100-| 25-x | = 40$
⇒ $| 25-x | =100-40$
⇒ $| 25-x | =60$
⇒ \(\left[ \begin{array}{l}25-x=60\\25-x=-60\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=25-60\\x=25-(-60)\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=-35\\x=85\end{array} \right.\)
c. $|2x+1| = | 23-x |$
⇒ \(\left[ \begin{array}{l}2x+1=23-x\\2x+1=-(23-x)\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}2x+x=23-1\\2x+1=-23+x\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}3x=22\\2x-x=-23-1\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=\frac{22}{3}\\x=-24\end{array} \right.\)
d. $|11-7x| – | 4x + 3|=0$
⇒ $|11-7x| = | 4x + 3|$
⇒ \(\left[ \begin{array}{l}11-7x=4x+3\\11-7x=-(4x+3)\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}-7x-4x=3-11\\11-7x=-4x-3\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}-11x=-8\\4x-7x=-3-11\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=\frac{8}{11}\\-3x=-14\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=\frac{8}{11}\\x=\frac{14}{3}\end{array} \right.\)
Giải thích các bước giải:
a,|x + 5| = 100
=> x + 5 = -100
x + 5 = 100
TH1: x + 5 = -100
x = (-100) – 5
x = -105
TH2 : x + 5 = 100
x = 100 – 5
x = 95
b,100 – I25 – xI = 40
100 – 40 = I25 – xI
60 = I25 – xI
=> 25 – x = 60
25 – x = -60
TH1: 25 – x = 60
x = 25 – 60
x = -35
TH2 : 25 – x = -60
x = 25 – (-60)
x = -85