Find the solution set for \(3a - 5 = -6a + 1\)

Solve \(\displaystyle\frac{2}{3}x+\displaystyle\frac{1}{2}= \displaystyle-\frac{3}{8}\)

Solve \(0.06x+0.05(10,000-x)=560\)

Solve \(8-3(4x-2)+5x=35\)

Solve \(x^2 -2x-24=0\)

Solve \(100x^2 =300x\)

Solve \((x-2)(x+1)=4\)

Solve \(x^3 +2x^2 -9x-18=0\)

A boat is traveling upstream against a current. If the speed of the boat in still water is \(r\) and the speed of the current is \(c\) then the formula for the distance traveled by the boat is \(d=(r-c) \cdot t\) where \(t\) is time. Find \(c\) if \(d=52\) miles, \(r=16\) miles, and \(t=4\) hours.

If an object is projected into the air with an initial velocity \(v\), its height \(h\) after \(t\) seconds will be given by \(h=vt-16t^2\). Find \(t\) if \(v=64\) feet/second and \(h=48\) feet.

Given the formula \(P=2w+2l\), solve for \(w\).

Solve for \(x\); \(ax-3=bx+5\)

Solve \(2(3x-4)=3+6x\)

Solve \(-15+3x=3(x-5)\)

A manufacturer of calculators knows that the number of calculators she can sell each week is related to the price by the equation \(x=1,300-100p\), where \(x\) is the number of calculators and \(p\) is the price per calculator. What price should she charge if she wants the weekly revenue to be \(\$4,000\)?

Solve \((2x-3)^2=25\)

The vertical rise of the Forest Double chair lift is \(1,170\) feet and the length of the chair lift is \(5,750\) feet. To the nearest foot, find the horizontal distance covered by a person riding this lift.

Solve \(x^2-6x+5=0\)

Solve by completing the square: \(x^2+5x-2=0\)

Solve \(x^2-5x-6=0\)

Solve \(x^2-6x=-7\)

Solve \(\displaystyle\frac{1}{10}x^2-\displaystyle\frac{1}{5}x=-\displaystyle\frac{1}{2}\)

Solve \((2x-3)(2x-1)=-4\)

If the shortest side in a \(30^\circ-60^\circ-90^\circ\) triangle is 1 inch, find the lengths of the other two sides.

If an object is thrown downward with an initial velocity of \(20\) feet per second, the distance \(s(t)\), in feet it travels in \(t\) seconds is given by the function \(s(t)=20t+16t^2\). How long does it take the object to fall \(40\) feet?

A company produces and sells copies of an accounting program for home computers. The total weekly cost to produce \(x\) copies of the program is \(C(x)=8x+500\), and the weekly revenue for selling all \(x\) copies of the program is \(R(x)=35x-0.1x^2\). How many programs must be sold for the weekly profit to be \(\$1,200\)?

Solve \((x+3)^2-2(x+3)-8=0\)

Solve \(27t^3-8=0\)

Solve \(4x^4+7x^2=2\)

Solve \(\displaystyle\frac{6}{a-4}=\displaystyle\frac{3}{8}\)

Solve \(\displaystyle\frac{x}{x-2}+\displaystyle\frac{2}{3}=\displaystyle\frac{2}{x-2}\)

Solve: \(\frac{1}{x+2} - \frac{1}{x} = \frac{1}{3}\)

Solve \(3+\displaystyle\frac{1}{x}=\displaystyle\frac{10}{x^2}\)

Solve for \(y\): \(\displaystyle\frac{y-4}{x-5}=3\)

Solve for \(y\): \(x=\displaystyle\frac{y-4}{y-2}\)

Solve for \(x\): \(\sqrt{3x+4}=5\)

Solve \(\sqrt{5x-1}+3=7\)

Solve: \(t+5=\sqrt{t+7}\)

Solve: \(\sqrt{x-3}=\sqrt{x}-3\)

The length of a rectangle is \(3\) inches less than twice the width. The perimeter is \(45\) inches. Find the length and width.

A person invests \(\$10,000\) in two accounts. One account earns a \(5\%\) annually, and the other earns \(6\%\). If the total interest earned in a year is \(\$560\), how much is invested in each account?

The lengths of the three sides of a right triangle are given by three consecutive integers. Find the lengths of the three sides.

Two families go on a ski trip. The first family makes the \(455\)-mile trip \(5\) miles per hour faster than the second family. The second family takes a half-hour longer. What were the speeds of the two families?

An inlet pipe can fill a pool in \(10\) hours and the drain can empty it in \(12\) hours. If the pool is empty and both the inlet pipe and drain are open, how long will it take to fill the pool?

Solve and graph: \(3x+3 < 2x-1\)

Solve: \(\, -2y-3 \leq 7\)

Solve \(\, 3(2x-4)-7x \leq -3x\)

Graph \(\, \{x \mid x \leq -2\) or \(x>3\}\)

Graph \(\, \{x \mid x > -1\) and \(x < 2\}\)

Solve and graph: \(\, -3 \leq 2x-5 \leq 3\)

Solve \(3t+7 \leq -4\) or \(3t+7 \geq 4\)

Solve \(x^2-2x-8 \leq 0\)

Solve \(x^2-6x+9\geq 0\)

Solve \(\displaystyle\frac{x-4}{x+1}\leq 0\)

Solve \(\displaystyle\frac{3}{x-2}-\displaystyle\frac{2}{x-3}>0\)

The USGS gives the survival rates for the ’Apapane as

\(0.72 \pm 0.11\) for adults
\(0.13 \pm 0.07\) for juveniles

Write each survival rate as an inequality involving percent.

A company that manufactures ink cartridges finds that they can sell \(x\) cartridges each week at \(p\) dollars, according to \(x=1,300-100p\). What price should they charge if they want to sell at least \(300\) cartridges?

The formula \(F=\dfrac{9}{5}C+32\) gives the relationship between Celsius and Fahrenheit. If the temperature on a certain day is \(86^\circ\) Fahrenheit, what is the temperature in degrees Celsius?

Solve \(\lvert x \rvert =5\)

Solve \(\lvert 2a-1 \rvert =7\)

Solve \(\left\lvert \frac{2}{3}x-3 \right| +5=12\)

Solve \(\lvert 3a-6 \rvert =-4\)

Solve \(\lvert 3a+2 \rvert = \lvert 2a+3 \rvert\)

Solve \(\lvert x-5 \rvert = \lvert x-7 \rvert\)

Graph \(\lvert 2x-5 \rvert < 3\)

Graph \(\lvert 4t-3 \rvert \geq 9\)

Graph \(\lvert 2x+3 \rvert +4 < 9\)

Graph \(\lvert 4-2t \rvert > 2\)

Solve \(\lvert 7y-1\rvert < -2\)

Solve \(\lvert 6x+2 \rvert > -5\)