....An important idea is solving system of equations

• This Regent's site works through solving systems of linear equation using various methods.  You will find it comprehensive.
• This is a tutorial from College Algebra.

...Another concept is using factoring to simplify rational algebraic expressions and solve rational equations

• This tutorial from College Algebra is about simplifying rational expressions.
• Purplemath has additional information on rational expressions.
• For a more complete explanation with sample problems go to http://regentsprep.org/Regents/mathb/mathb-topic.cfm?TopicCode=2B2
• Purplemath has an explanation for solving rational equations.
• This tutorial from College Algebra is about solving rational equations.

Beginning Algebra

192 Objectives

Sample Problem

Worktext Section

I. Real Numbers

II. Solving Linear Equations

alge169: Solving an inequality involving absolute value

2.25

alge170: Solving an inequality involving absolute value: Basic

Graph, on the number line, all points x for which

2.26

III. Graphs and Functions

See Pies 1 and 2

IV. Systems of Linear Equations

A. Solving and graphing

alge076: Solving a system of linear equations

Find the unique values of x and y satisfying the following system of equations:
x + 5y = –9
–7x – 4y = 6

2.31

alge079: Graphing a system of linear inequalities

Draw the solution to the system of inequalities
y> 5x – 8
y > – 2x – 5

3.23

B. Applications

alge224: Word problem on systems of linear equations: Problem type 3

Flying against the jet stream, a jet travels 4320 km in 8 hours. Flying with the jet stream, the same jet travels 9360 km in 9 hours. What is the speed of the jet in still air, and what is the speed of the jet stream?

2.35

alge184: Word problem on systems of linear equations: Problem type 2

Advance tickets to a show cost $35, same-day tickets cost $40. The total number of tickets sold was 60, for total receipts of $2200. How many tickets of each type were sold?

2.34

alge192: Word problem on systems of linear equations: Problem type 4

There are two tanks containing different alcohol solutions, one with 70% alcohol and the other with 95% alcohol. To obtain 70 gallons of solution at 90% alcohol, how many gallons must be used from each of the two tanks?

2.36

alge172: Word problem on systems of linear equations: Problem type 5

A theater group made appearances in two cities. The hotel charges before tax in the second city were $500 higher than in the first. The tax on the hotel bill was 8.5% in the first city and 4% in the second. After the trip, the total tax paid on accommodation expenses was $488.75. How much was the hotel bill in the first city before tax?

V. Exponents and Polynomials

See Pies 1 and 2

VI. Rational expressions and functions

A. Simplifying expressions

alge226: Adding rational expressions with different denominators

Write 

as a single rational expression.

5.14

alge682: Simplifying a ratio of polynomials: Problem type 2

Reduce the following quotient to lowest terms:

6.23

B. Solving equations

alge212: Solving a rational equation that simplifies to a quadratic equation: Problem type 1

Find all values of t satisfying the equation

5.21

Answer:
Find the least common denominator of all rational expressions and multiply through by LCD

Answer:

VII. Radicals and rational exponents

alge080: Simplifying a product of radical expressions: Problem type 1

Multiply out and simplify as much as possible:

7.3

Simplify. 

Answer:

Arith 6.4

alge086: Rationalizing the denominator of a radical expression

Rationalize the denominator and simplify:

7.6

alge089: Solving an equation with radicals: Problem type 1

Solve for u:  where u is a real number.

7.10

alge092: Even root property

alge093: Odd root property

alge227: Solve an equation with exponent using even-root property

alge228: Solve an equation with exponent using odd-root property