\(\left|x+15\right|+1=3x\)
\(\Leftrightarrow\left|x+15\right|=3x-1\)
\(\Rightarrow\orbr{\begin{cases}x+15=3x-1\\x+15=1-3x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-3x=-1-15\\x+3x=1-15\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}-2x=-16\\4x=-14\end{cases}\Leftrightarrow\orbr{\begin{cases}x=8\\x=\frac{-7}{2}\end{cases}}}\)
\(\left|x+15\right|+1=3x\)
\(\Rightarrow\left|x+15\right|=3x-1\left(1\right)\)
Nếu \(3x-1\ge0\)
\(\Rightarrow3x\ge1\)
\(\Rightarrow x\ge\frac{1}{3}\)
Khi đó (1) <=> \(\left|x+15\right|=3x-1\)
\(\Rightarrow\orbr{\begin{cases}x+15=3x-1\\x+15=-\left(3x-1\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-3x=-15-1\\x+15=-3x+1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-3x=-16\\x+3x=-15+1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}-2x=-16\\4x=-14\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\left(-16\right):\left(-2\right)\\x=\left(-14\right):4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=8\left(TM\right)\\x=-\frac{7}{2}\left(\text{loại}\right)\end{cases}}\)
Vậy x = 8
Bài giải
\(\left|x+15\right|+1=3x\)
* Nếu \(x+15< 0\) \(\Rightarrow\text{ }x< -15\) ta có :
\(-\left(x+15\right)+1=3x\)
\(-x-15+1=3x\)
\(-x-14=3x\)
\(-x-3x=14\)
\(x\left(-1-3\right)=14\)
\(x\cdot\left(-4\right)=14\)
\(x=\frac{7}{-2}\text{ ( Loại vì }\frac{7}{-2}>-15\text{ ) }\)
* Nếu \(x+15\ge0\) \(\Rightarrow\text{ }x\ge-15\) ta có :
\(x+15+1=3x\)
\(x+16=3x\)
\(3x-x=16\)
\(2x=16\)
\(x=16\text{ : }2\)
\(x=8\text{ ( Thỏa mãn ) }\)
\(\text{Vậy }x=8\)
Bài giải
\(\left|x+15\right|+1=3x\)
* Nếu \(x+15< 0\) \(\Rightarrow\text{ }x< -15\) ta có :
\(-\left(x+15\right)+1=3x\)
\(-x-15+1=3x\)
\(-x-14=3x\)
\(-x-3x=14\)
\(x\left(-1-3\right)=14\)
\(x\cdot\left(-4\right)=14\)
\(x=\frac{7}{-2}\text{ ( Loại vì }\frac{7}{-2}>-15\text{ ) }\)
* Nếu \(x+15\ge0\) \(\Rightarrow\text{ }x\ge-15\) ta có :
\(x+15+1=3x\)
\(x+16=3x\)
\(3x-x=16\)
\(2x=16\)
\(x=16\text{ : }2\)
\(x=8\text{ ( Thỏa mãn ) }\)
\(\text{Vậy }x=8\)
