Solve: StartFraction 2 Over 3 EndFraction minus 4 x plus StartFraction 7 Over 2 EndFraction equals negative 9 x plus StartFraction 5 Over 6. EndFraction. – 4x + = –9x +

Accepted Solution

Answer: [tex]x=-\frac{2}{3}[/tex]Step-by-step explanation: Given the following equation: [tex]\frac{2}{3}-4x+\frac{7}{2}=-9x+\frac{5}{6}[/tex] We need to solve for "x": 1. Move the fractions to one side of the equation and the x-terms to the other side: [tex]-4x+9x=\frac{5}{6}-\frac{2}{3}-\frac{7}{2}[/tex] 2. Add the like terms. To add the fractions we must find the Least Common Denominator (LCD): [tex]6=2*3\\3=3\\2=2\\\\LCD=2*3=6[/tex] Then: [tex]5x=\frac{5-4-21}{6}\\\\5x=-\frac{20}{6}\\\\5x=-\frac{10}{3}[/tex] 3. Finally, divide both sides of the equation by 5: [tex]\frac{5x}{5}=\frac{-\frac{10}{3}}{5}\\\\x=-\frac{2}{3}[/tex]