Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. 3x(x−1)=x+63x(x−1)=x+6

Question
Equations and inequalities
asked 2021-01-27
Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. \(3x(x−1)=x+63x(x−1)=x+6\)

Answers (1)

2021-01-28
\(3x(x-l)=2+6\)
Apply the distributive property \(3x^{2}-3x=x+6\)
Subtract «+ 6 from each side \(3x^{2}-3x—x-6=0\)
\(3x^{2}-4x-6=0\)
By the quadratic formula \(x=\frac{-(-4)\pm \sqrt{(-4)^2-4(3)(-6)}}{2(3)}\)
\(x=\frac{4\pm\sqrt88}6=\frac{4\pm\sqrt4*22}6)\)
\(x=\frac{4}{6}\pm\frac{2\sqrt{22}}6\)
\(x=\frac{2}{3}\pm \frac{\sqrt{22}}{3}\)
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