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# Algebra

# Algebra II

- Basic concepts
- Polynomials
- Polynomial multiplication
- Polynomial divide by Monomial
- Algebra of fractions
- Complex fractions
- One variable Equation
- two variables equations
- Inequalities
- Draw the graph of an absolute equation
- Word problem solving example 1
- Word problem solving example 2
- First degree equation examples
- Polynomial examples
- First degree equation applications
- Two variable equation examples
- First degree inequality examples
- Absolute value equation examples
- Absolute value inequality examples

**There are many things in real word can be expressed as an algebra expression**
For example, John bought three apples and five pears, let A represents apple and P represents pear, the algebra expression of total fruits is 3A + 5P. If an apple cost $0.76 which is A and a pear cost $0.56 which is P, then total cost to buy
these fruits will be (3 × $0.76) + (5 × $0.56) = $5.08. So algebra is related to quantity of an object and relationship between different objects.
We need to find the relationship between different objects. The following is an example of using algebra equation to solve a real word problem.
In a school laboratory, one solution containing 8% concentration of acid and a second solution containing 18% concentration of acid. Now we
need 20 milliliters of a solution containing a 12% concentration of acid, how many milliliters of each solution should be mixed to obtain the
solution we wanted? Now we use the algebra method to solve this problem. Let x be the number of milliliters of the first solution,
then (20 – x) is the number of milliliters of the second solution. The milliliters of acid in first solution is 8%x, the milliliters of acid
in second solution is 18%(20 – x), the milliliters of acid in mixture solution is 12%(20). Because the amount of acid in the mixture is the sum
of the amount of acid in the two solutions, so the equation is 8%x + 18%(20 – x) = 12%(20), solve this equation, we get x = 12,
Therefore, 12 milliliters of the first solution and 20 – 12 = 8 milliliters of the second solution should be mixed to get the solution we need.
So practice algebra can help us observe the relationship between different objects and learn the methods to solve real world problems.

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