Question

Tính x:

\(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|=10x\)

Answer 1

\(x=\dfrac{5}{3}\)

Cách giải : Nhập biểu thức đó vào máy tính casio bấm :

\(SHIFT+CALC\) rồi bấm phím \(=\)

Answer 2

\(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|=10x\)

\(\Leftrightarrow\left|4x+10\right|=10x\)

\(\Leftrightarrow\left|4x+10\right|-10x=0\)

\(\Leftrightarrow-6x+10=0\)

\(\Rightarrow x=\dfrac{5}{3}\)

Chúc bạn học tốt

Answer 3

Do \(\left|x+1\right|\ge0;\left|x+2\right|\ge0;\left|x+3\right|\ge0;\left|x+4\right|\ge0\forall x\)

\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|\ge0\forall x\)

mà \(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|=10x\) (1)

\(\Rightarrow10x\ge0\forall x\Rightarrow x\ge0\forall x\)

\(\Rightarrow x+1>0;x+2>0;x+3>0;x+4>0\)

\(\Rightarrow x+1=\left|x+1\right|;x+2=\left|x+2\right|;x+3=\left|x+3\right|;x+4=\left|x+4\right|\left(3\right)\)

Từ (1) và (3) =>x + 1 + x + 2 + x + 3 + x + 4 = 10x

=> 4x + 10 = 10x => 6x = 10

\(\Rightarrow x=\dfrac{10}{6}=\dfrac{5}{3}\) (TM)

Vậy....

Answer 4

Ko có cách làm hả Dương Phan Khánh Phan

Answer 5

Do

\(\left|x+1\right|\ge0\) \(\forall x\)

\(\left|x+2\right|\ge0\) \(\forall x\)

\(\left|x+3\right|\ge0\) \(\forall x\)

\(\left|x+4\right|\ge0\) \(\forall x\)

\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+|x+4|\ge0, \) \(\forall x\)

mà\(.\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+|x+4|=10x\)

\(\Rightarrow10x\ge0\) \(\forall x\) \(\Rightarrow x\ge0\)\(\forall x\)

\(\Rightarrow\) x+1+x+2+x+3+x+4=10x

\(\Leftrightarrow\) 4x+10=10x

\(\Leftrightarrow10x-4x=10\Leftrightarrow6x=10\Leftrightarrow x=\dfrac{5}{3}\)