Flashcards in Algebra Deck (10):
a. Sum of terms that are each powers of x multiplies by coefficients.
b. No dividing by variables!
c. No negative exponents or fractional exponents.
a. Highest power of variable is 2
a. Highest power of variable is 1
Simplifying using common factors
a. If there are common factors in the numerator and denominator of an expression, they can be divided out, provided that they are not equal to zero.
Multiplying algebraic expressions
a. To multiply two algebraic expressions, each term of one expression is multiplied by each term of the other expression.
i. 2 + x = 3
ii. 4 + 2x = 6
iii. 3x – y = 6
iv. 6x – 2y = 12
Solving linear equations with one unknown
1. Simply isolate the single variable onto one side of the equation by performing the same operation on both sides.
Solving two linear equations with two unknowns.
1. Ex: 3x + 4y = 17
2. Ex: 6x +8y = 35
3. If a contradiction is reached ( 6x + 8y = 34 ) then there is no solution between the two equations.
4. If a trivial solution is reached such as 0 = 0 then the equations are equivalent and have infinitely many solutions.
5. Otherwise a unique solution can be found.
a. Expressing one unknown in terms of the other
b. Eliminating one of the unknowns by creating equal coefficients for one of the variables and adding the equations.
Solving linear inequalities
a. The unknown is isolated on one side of the equation
b. Multiplying or dividing an inequality by a negative number reverses the order of the inequality.