# Solve the equations and inequalities below. Check your solution(s), if possible. a.300x-1500=2400 b.(3/2)^{x}=(5/6)^{x}+2 c.x^{2}-25leq 0 d.|3x-2|>4

Question
Equations and inequalities
Solve the equations and inequalities below. Check your solution(s), if possible. $$a.300x-1500=2400$$
$$b.(3/2)^{x}=(5/6)^{x}+2$$
$$c.x^{2}-25\leq 0$$
$$d.|3x-2|>4$$

2021-02-09
$$a.x=13$$
$$b.x=3$$
$$c.-5\leq x\leq 5$$
$$d.x<-\frac{2}{3} or x>2$$

### Relevant Questions

Solve the equations and inequalities below. Check your solution(s), if possible. $$\displaystyle{a}{.300}{x}-{1500}={2400}$$
$$\displaystyle{b}.{\left(\frac{{3}}{{2}}\right)}^{{{x}}}={\left(\frac{{5}}{{6}}\right)}^{{{x}}}+{2}$$
$$\displaystyle{c}.{x}^{{{2}}}-{25}\leq{0}$$
$$\displaystyle{d}.{\left|{3}{x}-{2}\right|}{>}{4}$$
Solve the equation 300x-1500=2400
Solve the equations and inequalities. Find the solution sets to the inequalities in interval notation. $$\displaystyle{3}{x}{\left({x}-{1}\right)}={x}+{6}$$
Solve the following equations and inequalities for x. Check your solution(s), if possible $$a. \frac{3}{x}=9$$
$$b. \sqrt x=4$$
$$c. x^{2}=25$$
$$d. 2(x−3)>4$$
Solve the following equations and inequalities for x. Check your solution(s), if possible $$\displaystyle{a}.{\frac{{{3}}}{{{x}}}}={9}$$
$$\displaystyle{b}.\sqrt{{x}}={4}$$
$$\displaystyle{c}.{x}^{{{2}}}={25}$$
$$\displaystyle{d}.{2}{\left({x}−{3}\right)}{>}{4}$$
Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\displaystyle{\left({x}^{{2}}-{9}\right)}^{{2}}-{2}{\left({x}^{{2}}-{9}\right)}-{35}={0}$$
Solve the equations and inequalities below, if possible. $$\displaystyle{a}.\sqrt{{{x}−{1}}}+{13}={13}$$
$$\displaystyle{b}.{6}{\left|{x}\right|}{>}{18}$$
$$\displaystyle{c}.{\left|{3}{x}-{2}\right|}\le{2}$$
$$\displaystyle{d}.{\frac{{{4}}}{{{5}}}}-{\frac{{{2}{x}}}{{{3}}}}={\frac{{{3}}}{{{10}}}}$$
$$\displaystyle{e}.{\left({4}{x}-{2}\right)}^{{{2}}}\le{100}$$
$$\displaystyle{f}.{\left({x}-{1}\right)}^{{{3}}}={8}$$
Solve the equations and inequalities. Find the solution sets to the inequalities in interval notation. $$\displaystyle\sqrt{{{t}+{3}}}+{4}={t}+{1}$$
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors $$\displaystyle\hat{{{i}}}$$ and $$\displaystyle\hat{{{j}}}$$.
1. (Enter in box 1) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+{\left({E}{n}{t}{e}{r}\in{b}\otimes{2}\right)}{P}{S}{K}\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+$$
5. ( Enter in box 5) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
Solve the equations and inequalities below, if possible. Check your solutions. $$\displaystyle{a}.{\left({4}{x}−{2}\right)}^{{{2}}}≤{100}$$
$$\displaystyle{b}.{\left({x}−{1}\right)}^{{{2}}}={9}$$
$$\displaystyle{c}.{x}^{{{2}}}+{x}−{20}{<}{0}$$
$$\displaystyle{d}{.2}{x}^{{{2}}}−{6}{x}=−{5}$$