Question

Tìm x biết:

a) 11 - (|x| - 7) = -21

b) -5 + (|x| + 13) = |-4|

c) |x| - 300 = -190

d) -261 + |x| = 315

Answer 1

a) \(11-\left(\left|x\right|-7\right)=-21\)

=> \(\left|x\right|-7=11-\left(-21\right)\)

=> \(\left|x\right|-7=32\)

=> \(\left|x\right|=32+7\)

=> \(\left|x\right|=49\)

=> \(\left[{}\begin{matrix}x=49\\x=-49\end{matrix}\right.\)

Vậy \(x=\left[{}\begin{matrix}49\\-49\end{matrix}\right.\)

b) \(-5+\left(\left|x\right|+13\right)=\left|-4\right|\)

=> \(-5+\left(\left|x\right|+13\right)=4\)

=> \(\left|x\right|+13=4-\left(-5\right)\)

=> \(\left|x\right|+13=9\)

=> \(\left|x\right|=9-13\)

=> \(\left|x\right|=-4\)

mà \(\left|x\right|\le x\)

=> \(x=\varnothing\)

Vậy \(x=\varnothing\)

Answer 2

c) \(\left|x\right|-300=-190\)

=> \(\left|x\right|=-190+300\)

=> \(\left|x\right|=110\)

=> \(\left[{}\begin{matrix}x=100\\x=-100\end{matrix}\right.\)

Vậy \(x=\left[{}\begin{matrix}100\\-100\end{matrix}\right.\)

d) \(-261+\left|x\right|=315\)

=> \(\left|x\right|=315-\left(-261\right)\)

=> \(\left|x\right|=576\)

=> \(\left[{}\begin{matrix}x=576\\x=-576\end{matrix}\right.\)

Vậy \(x=\left[{}\begin{matrix}576\\-576\end{matrix}\right.\)