Improve Your Algebra Skills with Practice Problems

The given set of equations has no solution or infinitely many solutions.
Given: ${\displaystyle 6xy\le 24\text{and}6x-y>24}$ are the given set of inequalities.

Reduce each fraction to lowest terms
${\displaystyle \frac{12}{16}}$

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be ${\displaystyle 0.03\frac{m^3}{s}}$, determine mechanical power that is converted to thermal energy during this process due to frictional effects.

Solve the following equations and inequalities.
1. ${\displaystyle \log (3x-1)=\log (4-x)}$
2. ${\displaystyle {\log }_2{x}^3={\log }_2\left(x\right)}$
3. ${\displaystyle \ln 8-x^2=\ln (2-x)}$
4. ${\displaystyle {\log }_{5}18-x^2={\log }_5(6-x)}$

To fill: The blank with right inequality sign for the system of inequalities has NO solution.
Given information: It is given that the inequalities ${\displaystyle y-2x\le 4}$ and ${\displaystyle 6x-3y_{-12}}$

The equation
${\displaystyle \frac{x}{4}=2+\frac{x-3}{3}}$
can be solved by multiplying both sides by the__________ of the fractions, which is________

use the properties of logarithms, given that ${\displaystyle \ln \left(2\right)\approx 0.6931\text{ and }\ln \left(3\right)\approx 1.0986}$ to approximate the logarithm. Use a calculator to confirm your approximations.
(a) ${\displaystyle \ln \left(0.75\right)\approx }$
(b) ${\displaystyle \ln \left(288\right)\approx }$
(c) ${\displaystyle \ln \left(\sqrt{3}\left\{24\right\}\right)\approx }$
(d) ${\displaystyle \ln \left(\frac{1}{6}\right)\approx }$

Which of following expressions are equivalent to ${\displaystyle \frac{3}{n}+\frac{2}{6n^2+12n}?}$
a) ${\displaystyle \frac{18n+38}{6n(n+2)}}$
b) ${\displaystyle \frac{5}{6n^2+13n}}$
c) ${\displaystyle \frac{18(n+2)}{6n(n+2)}+\frac{2}{6n(n+2)}}$
d) ${\displaystyle \frac{3(6n^2+12n)+2n}{n(6n^2+12n)}}$

perform the indicated operations and express the answers in simplified form
${\displaystyle \frac{(x+3)}{10}+\frac{(2x+1)}{15}-\frac{(x-2)}{18}}$

Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
${\displaystyle \frac{x-14}{x^2-3x}}$

Solve each equation. ${\displaystyle s^2-4s=21}$

For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation.
${\displaystyle \sqrt{t+3}+4=t+1}$

What are partial fractions?

Solve the equation
${\displaystyle \frac{x+1}{x-1}=\frac{-10}{x+3}+\frac{8}{x^2+2x-3}}$

Solving equations and inequalities:
Janet, an experienced shipping clerk can fill a certain order in 2 hours. Jim a new clerk, needs to do the same job in 3 hours. Working together how long will it take them to fill the order?

How linear functions, linear equations and linear inequalities are related.

Tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not.
${\displaystyle 2x^3}$

let ${\displaystyle u=[2,-1,-4],v=[0,0,0]}$, and ${\displaystyle w=[-6,-9,8]}$. we want to determine by inspection (with minimal compulation) if ${\displaystyle \{u,v,w\}}$ is linearly dependent or independent. choose the best answer:
A. The set is linearly dependent because one of the vectors is a scalar multiple of another vector.
B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other.
C. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space.
D. The set is linearly dependent because two of the vectors are the same.
E. The set is linearly dependent because one of the vectors is the zero vector.
F. We cannot easily tell if the set is linearly dependent or linearly independent.