+118654 |6-5x|=3x-7
\(3x-7>0\\ 3x>7\\ x>2.\dot3\\~\\ (6-5x)^2=(3x-7)^2\\ 36+25x^2-60x=9x^2-42x+49\\ 25x^2-9x^2-60x+42x+36-49=0\\ 16x^2-18x-13=0\\ x=\frac{18\pm\sqrt{324+4*16*13}}{32}\\ x=\frac{18\pm34}{32}\\ x=\frac{18+34}{32}\qquad or \qquad x=\frac{18-34}{32}\\ x=\frac{52}{32}\qquad or \qquad x=\frac{-16}{32}\\ x=1.625 \qquad or \qquad x=\frac{-1}{2}\\ But\;\; x>2.\dot3\qquad \text{ No solution} \)
+118654 |6-5x|=3x-7
This is an easier way ://
\(3x-7>0\\ 3x>7\\ x>2.\dot3\\~\\ 6-5x=3x-7 \qquad or \qquad -(6-5x)=3x-7\\ -8x=-13 \qquad \qquad or \qquad -6+5x=3x-7\\ x=1.624 \qquad \qquad or \qquad 2x=-1\\ x=1.624 \qquad \qquad or \qquad x=-0.5\\ \text{But since }x>2.\dot3\quad \text{there are no real solutions}\)
