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

Equations and inequalities
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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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