POPULAR ALGEBRAIC TECHNIQUES

1) Combining like terms and simplifing.

Example: Subtract -4x⁴-5x³+2x²-22 from 7x⁴-3x³+7x²-32x+17

Solution: Form the difference & simplify

7x⁴-3x³+7x²-32x+17 - (-4x⁴-5x³+2x²-22) = 7x⁴-3x³+7x²-32x+17+4x⁴+5x³-2x²+22
= 11x⁴+2x³+5x²-32x+39

2) Solving quadratic equations by factoring.

Example: Solve: 6x²-16x-70=0

Solution: divide both sides by 2 to get: 3x²-8x-35=0

factor the left side of the equaiton: (3x+7)(x-5)=0

set each factor equal to zero: 3x+7=0, x-5=0

solve each linear equation for x: x= -7/3, x=5

3) Solving simple linear inequalities.

Note: Inequalities are expressions involving the symbols for "greater than", "less than", greater than or equal to",
"less than or equal to". Solve these for x the same way you would solve equations with one exception. If you
multiply or divide by a negative quantity, the inequality reverses direction. In most basic types, you can avoid
this in the process of solving for x.

Example: Solve for x: 7-5x >0 (start by adding 5x to both sides to avoid dividing by -5 while solving for x)

Solution: 7 > 5x
7/5 > x (dividing both sides by 5) (the inequality does not have to be reversed)
reading the inequality from right to left, "x is less than 7/5"

4) Solving simple equations for a given quantity.

Example: Solve the following equation for b: 5ac - 10bc = 15c

Solution: divide both sides by 5c as long as c does not take on the value of zero.
a - 2b = 3.
add 2b to both sides: a = 2b +3
subtact 3 from both sides: a - 3 =2b
divide both sides by 2: (a - 3)/2 = b

5) Most other techniques used in the course will be covered in my lessons and those that involve the TI-83 calculator will be covered in detail as they come up during the course.