# Solve the equations and inequalities below, if possible. Check your solutions. a.(4x−2)^{2}≤100 b.(x−1)^{2}=9 c. x^{2}+x−20<0 d.2x^{2}−6x=−5

Question
Equations and inequalities
Solve the equations and inequalities below, if possible. Check your solutions. $$\displaystyle{a}.{\left({4}{x}−{2}\right)}^{{{2}}}≤{100}$$
$$\displaystyle{b}.{\left({x}−{1}\right)}^{{{2}}}={9}$$
$$\displaystyle{c}.{x}^{{{2}}}+{x}−{20}{<}{0}$$</span>
$$\displaystyle{d}{.2}{x}^{{{2}}}−{6}{x}=−{5}$$

2021-02-04
$$\displaystyle{a}.-{2}\leq{\left\lbrace{x}\right\rbrace}\leq{\left\lbrace{3}\right\rbrace}$$
$$\displaystyle{b}.{x}={4}{\quad\text{and}\quad}{x}=-{2}$$
$$\displaystyle{c}.-{5}{<}{x}{<}{4}$$</span>
$$\displaystyle{d}.{x}={1.5}\pm{0},{5}{i}$$

### Relevant Questions

Solve the equations and inequalities below, if possible. $$\displaystyle{a}.\sqrt{{{x}−{1}}}+{13}={13}$$
$$\displaystyle{b}.{6}{\left|{x}\right|}{>}{18}$$
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$$\displaystyle{d}.{\frac{{{4}}}{{{5}}}}-{\frac{{{2}{x}}}{{{3}}}}={\frac{{{3}}}{{{10}}}}$$
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A system of linear equations is given below.
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$$\displaystyle-{\frac{{{1}}}{{{2}}}}{x}+{3}={y}$$
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A. (0, -3)
B. (-6, 0)
C. There are infinite solutions.
D. There are no solutions.

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