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 2020-11-08
Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. \(\displaystyle{3}{x}{\left({x}−{1}\right)}={x}+{63}{x}{\left({x}−{1}\right)}={x}+{6}\)

Answers (1)

2020-11-09
\(\displaystyle{3}{x}{\left({x}-{l}\right)}={2}+{6}\)
Apply the distributive property \(\displaystyle{3}{x}^{{{2}}}-{3}{x}={x}+{6}\)
Subtract «+ 6 from each side \(\displaystyle{3}{x}^{{{2}}}-{3}{x}—{x}-{6}={0}\)
\(\displaystyle{3}{x}^{{{2}}}-{4}{x}-{6}={0}\)
By the quadratic formula \(\displaystyle{x}={\frac{{-{\left(-{4}\right)}\pm\sqrt{{{\left(-{4}\right)}^{{2}}-{4}{\left({3}\right)}{\left(-{6}\right)}}}}}{{{2}{\left({3}\right)}}}}\)
\(\displaystyle{x}={\frac{{{4}\pm\sqrt{{88}}}}{{6}}}={\frac{{{4}\pm\sqrt{{4}}\cdot{22}}}{{6}}}{)}\)
\(\displaystyle{x}={\frac{{{4}}}{{{6}}}}\pm{\frac{{{2}\sqrt{{{22}}}}}{{6}}}\)
\(\displaystyle{x}={\frac{{{2}}}{{{3}}}}\pm{\frac{{\sqrt{{{22}}}}}{{{3}}}}\)
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