Improve Your Algebra Skills with Practice Problems

There are some bicycles and tricycles beside a garden The garden attendant counted a total of 64 bicycles and tricycles.

For $abc=1$ prove that $\underset{\text{cyc}}{\sum <!--\; \sum \; -->}\frac{1}{a+3}\ge <!--\; \ge \; -->\underset{\text{cyc}}{\sum <!--\; \sum \; -->}\frac{a}{a^2+3}$
I tried TL, BW, the Vasc's Theorems and more, but without success.
I proved this inequality!
I proved also the hardest version: $\underset{cyc}{\sum <!--\; \sum \; -->}\frac{1}{a+4}\ge <!--\; \ge \; -->\underset{cyc}{\sum <!--\; \sum \; -->}\frac{a}{a^2+4}$
Thanks all!

Suppose that the functions s and t are defined for all real numbers x as follows. s(x) = 2x - 4 t(x) = 6x. Write the expressions for (s + t)(x) and (s*t)(x) and evaluate(s - t)(-1)

(s+t)(x)=
(s*t)(x)=
(s-t)(-1)=

Find the Lowest Common Denominator for $\frac{3x}{x^2+5x-<!--\; -\; -->24}$ and $\frac{x+1}{x^2-<!--\; -\; -->12x+27}$

how many years, to the nearest year, will it take money to quadruple if it is invested at 6% compounded annually?

Solve. $2y^2+9y-<!--\; -\; -->35÷<!--\; ÷\; -->y+7$

If 3 ordinary coins are tossed, write out a sample space.
Part of the sample space is the. Type 3 more outcomes for the sample.

How do i factor $12a^{2}b+30a{b}^2$

If $f(x)=3x^3-<!--\; -\; -->k{x}^2+x-<!--\; -\; -->7k$, find a number k such that the graph of f contains the point (-1,6).

Maliki Williams earned $48,000 from royalties on her cookbook. She paid a 28% income tax on these royalties. The balance was invested two ways. some of it at 3.25% interest and some at 1.75%.
The investment produced $904.80 interest per year. Find the amount invested at each rate.

Find the coordinates of points where the graph of
$f(x)=x^4-<!--\; -\; -->4x^3+8$
has horizontal tangents. As a check, graph f(x) and see whether the points you found look as though they have horizontal tangents.

$(256{)}^{0.16}\times <!--\; \times \; -->(256{)}^{0.09}=?$

$x=\frac{3}{4},y=-<!--\; -\; -->\frac{2}{3}$ Evaluate the variable expression x + y for the given values of x and y.

If y = 1/(x+1) , then what is x in terms of y?

Express f(f(x)) as a single simplified fraction.
f(x) = x/x+1

Add. Write your answer as a mixed number in simplest form.
$5\frac{3}{4}+3\frac{2}{7}$

1. 1. Solve the system of equations
x + 8y = 8
2x - 9y = -9
2. 2. If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why.
3x - 6y = 3
9x - 18y = 6
3. 3. If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. -4x + 6y = -5
18y = -15 + 12x
4. 4. Solve the system of equations. x + y = -1
x - y = 11
5. 5. Determine whether the given ordeblack pair is a solution to the system of equations.
(1, -2)
4x + y = 2
3x + 4y = -5
6. 6. Solve the system of equations. 4x + y = -13
6x + 5y = -9

Write the ratio: $\frac{2}{9}$ to $\frac{7}{9}$ as a fraction in lowest terms.

Simplify
$\frac{\frac{3}{8}-<!--\; -\; -->1}{\frac{7}{4}+1}$

$\frac{1}{3}(\frac{5}{6}+\frac{1}{2})\sim <!--\; \sim \; -->(\frac{1}{3}+\frac{5}{6})+2$