Question

[𝚈𝚊𝚔𝚒]

Tìm số nguyên x, biết :

a) |x| + 1 - (-4) = 5

b) |x| - (-2) = (-1)

c) 5 - |x+1| = 30

d) |x-2| = |23| và x < 0

e) |x+1| = |-2| và x > 0

f) |2-x| + 2 = x

giúp mk nha , tí nữa mk ik hk rùi !!!

Answer 1

[Despacito]

a) \(\left|x\right|+1-\left(-4\right)=5\)

\(\left|x\right|+1+4=5\)

\(\left|x\right|+5=5\)

\(\left|x\right|=0\)

\(\Rightarrow x=0\)

vậy \(x=0\)

b) \(\left|x\right|-\left(-2\right)=\left(-1\right)\)

\(\left|x\right|+2=-1\)

\(\left|x\right|=-3\)

\(\Rightarrow x\in\varnothing\)

vậy \(x\in\varnothing\)

c) \(5-\left|x+1\right|=30\)

\(\left|x+1\right|=5-30\)

\(\left|x+1\right|=-25\)

\(\Rightarrow x\in\varnothing\)

vậy \(x\in\varnothing\)

d) \(\left|x-2\right|=\left|23\right|\)

\(\left|x-2\right|=23\)

\(\Rightarrow\orbr{\begin{cases}x-2=23\\x-2=-23\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=25\\x=-21\end{cases}}\)

mà \(x< 0\)nên \(x=-21\)

vậy \(x=-21\)

e) \(\left|x+1\right|=\left|-2\right|\)

\(\left|x+1\right|=2\)

\(\Rightarrow\orbr{\begin{cases}x+1=2\\x+1=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=-3\end{cases}}\)

mà \(x>0\)nên \(x=1\)

vậy \(x=1\)

f) \(\left|2-x\right|+2=x\)

\(\left|2-x\right|=x-2\)

\(\Rightarrow\orbr{\begin{cases}2-x=x-2\\2-x=2-x\end{cases}}\Rightarrow\orbr{\begin{cases}0x=-4\\0x=0\end{cases}}\)

vậy \(\orbr{\begin{cases}x\in\varnothing\\\forall x\in R\end{cases}}\)