Question

Tìm x biết

Ix + 4/15I - I-3,75I = -I-2,15I 

CHÚ Ý: Dấu "IxI" là của giá trị tuyệt đối

Answer 1

\(\left|x+\frac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)

=> \(\left|x+\frac{4}{15}\right|-3,75=-2,15\)

=> \(\left|x+\frac{4}{15}\right|=\frac{8}{5}\)

+) \(x+\frac{4}{15}=\frac{8}{5}\)

=> \(x=\frac{8}{5}-\frac{4}{15}=\frac{24}{15}-\frac{4}{15}=\frac{20}{15}=\frac{4}{3}\)

+) \(x+\frac{4}{15}=-\frac{8}{5}\)

=> \(x=-\frac{8}{5}-\frac{4}{15}\)

=> \(x=-\frac{24}{15}-\frac{4}{15}=-\frac{28}{15}\)

Answer 2

\(|x+\frac{4}{15}|-|-3,75|=-|-2,15|\)

\(|x+\frac{4}{15}|-3,75=-2,15\)

\(|x+\frac{4}{15}|=-2,15+3,75\)

\(|x+\frac{4}{15}|=1,6\)

Ta có : \(|x+\frac{4}{15}|\ge0\forall x\)

\(\Rightarrow|x+\frac{4}{15}|=x+\frac{4}{15}\)

\(\Rightarrow x+\frac{4}{15}=1,6\)

\(x+\frac{4}{15}=\frac{8}{5}\)

\(x=\frac{8}{5}-\frac{4}{15}\)

\(x=\frac{4}{3}\)

Answer 3

\(|x+\frac{4}{15}|\)\(-|-3,75|=-|-2,15|\)

\(< = >|x+\frac{4}{15}|-3,75=-2,15\)

\(< =>\)\(|x+\frac{4}{15}|=1,6=\frac{8}{5}\)

\(< =>\orbr{\begin{cases}x=\frac{4}{3}\\x=-\frac{28}{15}\end{cases}}\)

Answer 4

| x + 4/15 | - | -3, 75 | = -| -2, 15 |

<=> | x + 4/15 | - 3, 75 = -2, 15

<=> | x + 4/15 | = 1, 6

<=> x + 4/15 = 1, 6 hoặc x + 4/15 = -1, 6

<=> x = 4/3 hoặc x = -28/15