Improve Your Algebra Skills with Practice Problems

How to add or subtract fractions with unlike denominators

I am having trouble with these type of problems. ${\displaystyle \frac{3}{5}(9y-4)+\frac{9}{16}(15y+12)}$ I cant figure out how to simplify with fractions?

Write an algebraic equation for the following problem and then solve it.
When Angela and Walker first started working for the supermarket, their weekly salaries totaled $500. Now during the last 25 years Walker has seen his weekly salary triple. Angela has seen her weekly salary become four times larger. Together their weekly salaries now total $1740. How much did they each make 25 years ago?
The algebraic equation is ___${\displaystyle =1740}$.

${\displaystyle \frac{1}{2}}$ divided by ${\displaystyle \frac{3}{5}}$

If the probability that an event will occur is ${\displaystyle \frac{2}{11}}$. (Enter your probabilities as fractions.)
(a) What are the odds in favor of the event occurring?
(b) What are the odds against the event occurring?

Among all pairs of numbers with a sum of 149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Tell whether each number in the list is a real number, a ratonal number, an irrational number, an integer, or a whole number. Then order the numbers from least to greatest.
${\displaystyle \sqrt{64},-5,\sqrt{9},2}$
-5, 2, 9, 64

Rewrite the equation below so that is does not have fractions ${\displaystyle \frac{2}{3}x+3=\frac{2}{7}}$ do not use decimals in your answer

Solve the following quadratic expressions by factoring. First write the expressions in completely factored form. Then write the real numer solutions.
[Hint: Remember to use proper notation when writing the real number solutions.For example: if the solutions are ${\displaystyle x=1}$ and ${\displaystyle x=4}$, write ${\displaystyle x=1,4}$.
1) ${\displaystyle x^2+9x+20=0}$
Factored form - ?
Real number solutions - ?
2) ${\displaystyle x^2-x-72=0}$
Factored form - ?
Real number solutions - ?
3) ${\displaystyle x^2-36=0}$
Factored form - ?
Real number solutions - ?
4) ${\displaystyle x^2-10x+25=0}$
Factored form - ?
Real number solutions - ?

Solve for B.
${\displaystyle 9B+C=A}$
${\displaystyle B=?}$

A piston–cylinder device initially contains ${\displaystyle 0.07m^3}$ of nitrogen gas at 130 kPa and ${\displaystyle {180}^{\circ }}$. The nitrogen is now expanded to a pressure of 80 kPa polytropically with a polytropic exponent whose value is equal to the specific heat ratio (called isentropic expansion). Determine the final temperature and the boundary work done during this process.

Ratio and proportion: ${\displaystyle 0.8:10::x:25}$

Write an equal decimal having the given number of decimal places. Briefly describe the Decimal Squares for both decimals in the equation.
a. ${\displaystyle 0.7=}$______(hundredths)
The Decimal Square for this decimal can be described by
A. 7 out of 10 parts shaded, or 70 out of 100 parts shaded.
B. 10 out of 7 parts shaded, or 100 out of 70 parts shaded.
C. 70 out of 10 parts shaded, or 7 out of 100 parts shaded.

In 2000. ${\displaystyle 54\mathrm{\%}}$ of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately ${\displaystyle 1.9\mathrm{\%}}$ per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, P(x), who regularly used the news outlet x years after 2000.
${\displaystyle P\left(x\right)=}$____________
(Use integers or decimals for any numbers in the expression.)

The total percent of individuals aged 16 to 24 enrolled in college as of October of each year who completed high school during the preceding 12 months is ${\displaystyle f\left(x\right)=66.925x^{0.043}}$, where x is the number of years after 1999.
a) Use this model to estimate the total percent in 2003 and 2007.
The total percent in 2003 is __%
The total percent in 2007 is __%

Write an equation that models the linear situation:
A submarine 560 feet below the surface comes up 2.5 feet per second.
Instructions:
Do not use any spaces between variables, constants, equals signs, and operation signs.
For example DO NOT enter ${\displaystyle f\left(x\right)=2x+1}$ DO ENTER: ${\displaystyle f\left(x\right)=2x+1}$
Put parentheses around constants that are fractions like this: ${\displaystyle y=\left(\frac{2}{3}\right)x-\left(\frac{1}{2}\right)}$
You may use decimals if the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4)
To write your equation, use the variables:
${\displaystyle t=}$ amount of time the submarine rises towards the surface (seconds)
${\displaystyle L\left(t\right)=}$ see-level-position of the submarine (feet).
Equation _________.

Translate this sentence into an equation.
23 less than Chrissys

The equations ${\displaystyle y=-x+4\text{and}y=12x-8y}$

$=21x-8$ form a system of linear equations.

The table below shows the y-value for each equation at six different values of x. $xy=-x+4y=12x-804-822-740-66-2-58-4-410-6-3$
What can you conclude from the table?

A. The system has one solution, when x=0.

B. The system has one solution, when x=4.

C. The system has one solution, when x=8.

D. The system has no solution.

Use the​ Gauss-Jordan method to solve the following system of equations.
${\displaystyle 3x-4y+4z=10}$
${\displaystyle 3x+5y-z=15}$
${\displaystyle 12x-7y+11z=45}$
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. The solution is ( _ , _ ,_ ) in the order​ x, y, z. ​(Simplify your​ answers.)
B. There is an infinite number of solutions. The solution is ( _ , _, _ ) where z is any real number. ​(Simplify your answers. Use integers or fractions for any numbers in the​ expressions.)
C. There is no solution.

A roof has a 0.4-inch layer of ice on it from a previous storm. Another ice storm begins to deposit ice at a rate of 0.26 inches per hour.
a) Find a formula for a linear function f that models the thickness of the ice on the roof x hours after the second ice storm started.
b) How thick is the ice after 3.5 hours?
a) ${\displaystyle f\left(x\right)=}$___
b) The ice is ___ inches thick after 3.5 hours.