Below is a comprehensive set of math questions covering algebra, systems of equations, absolute value equations and inequalities, rational equations, and complex numbers. Final answers are provided at the end of the page.
How much water should be added to \(20\) ounces of a \(20\%\) acid solution to reduce it to a \(10\%\) solution?
Solve for \(C\) in the equation
\[ B = 2BD + 2CE + 2CL \]Thomas can paint a house in \(6\) days, while Joe can paint the same house in \(12\) days. How long would it take Thomas and Joe, working together, to paint the house?
Solve the system of equations:
\[ \begin{cases} 3x - 4y = 25 \\ -2x + y = -10 \end{cases} \]An airliner travels \(3000\) miles with a tailwind in \(4\) hours and returns against the wind in \(4.8\) hours. Find the ground speed of the airliner.
Write the following as a single interval if possible:
\[ (-9,\,2) \cup (1,\,30) \]Solve the equation:
\[ |5x - 2| - 2 = 6 \]Solve the inequality:
\[ |4x + 6| < 30 \]Solve the inequality:
\[ |4x + 5| - 5 > 6 \]Solve the inequality:
\[ \sqrt{(3x - 2)^2} < 5 \]Solve the equation:
\[ |-2x + 5| = 2x - 5 \]Solve the equation:
\[ |4x - 2| = 8x - 12 \]Evaluate and write in standard form:
\[ (4 - 2i)(-3 + 3i), \quad \text{where } i^2 = -1 \]Evaluate and write in standard form:
\[ \frac{2 - 3i}{2 - 2i}, \quad \text{where } i^2 = -1 \]Evaluate and write in standard form:
\[ (-3 + 2i)^2 - 3(3 - i)(-2 + 2i), \quad \text{where } i^2 = -1 \]Solve the equation:
\[ -(x - 2)^2 - 2 = 7 \]Solve the equation:
\[ (-x + 3)^2 - 12 = 8 \]Solve the equation:
\[ 3 + \frac{30}{x^2} = -\frac{21}{x} \]Solve the equation:
\[ -\frac{x}{x^2 + 2x - 3} + \frac{5}{x + 3} = 1 \]The sum of a number and its reciprocal is \[ \frac{82}{9}. \] Find the number.
1) \(20\) ounces
2) \( C = \dfrac{B(1 - 2D)}{2E + 2L} \)
3) \(4\) days
4) \( (3,\,-4) \)
5) \(687.5\) miles/hour
6) \( (-9,\,30) \)
7) \( x = 2 \), \( x = -\dfrac{6}{5} \)
8) \( -9 < x < 6 \)
9) \( (-\infty,\,-4) \cup \left(\dfrac{3}{2},\,\infty\right) \)
10) \( (-1,\,\dfrac{7}{3}) \)
11) \( \left[\dfrac{5}{2},\,\infty\right) \)
12) \( x = \dfrac{5}{2} \)
13) \( -6 + 18i \)
14) \( \dfrac{5}{4} - \dfrac{i}{4} \)
15) \( 17 - 36i \)
16) \( x = 2 \pm 3i \)
17) \( x = 3 \pm 2\sqrt{5} \)
18) \( x = -2,\,-5 \)
19) \( x = 1 \pm i \)
20) \( x = 9 \) or \( x = \dfrac{1}{9} \)
More math questions and problems with detailed solutions are available on this site.