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Chapter 1 Notes
Algebra II
Myrick
Section 1.2 – Algebraic Expressions
Definition: A ___________ is a symbol, usually a letter, used to represent one or
more numbers.
Definition: When you substitute numbers for the variables in an algebraic
expression and follow order of operations, you ___________ the expression.
NOTE: When you evaluate, your answer should be a _______________.
Definition: Order of Operations
P–
E–
M–
D–
A–
S–
Example 1: Simplify by following order of operations.
-2(4 – 7) + 32
Example 2: Evaluate 7x  3xy for x  2 and y  5 .
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
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2
Example 3: Evaluate k 18  4k for k  6 .
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Chapter 1 Notes
Algebra II
Myrick
Definition: A ________ is
a) a number
Example 
b) a variable
Example 
c) the product of a number and one or more variables
Example 
Definition: The numerical factor in a term is the ________________.
Example 4: Draw a box around each term and an arrow pointing to each
coefficient.
2b 2  b  7bc
Definition: ________________ have the same variables raised to the same
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powers.
Example 5: Circle the like terms.
3x 2y
6xy
9xy 2
2x 2y 2
Example 6: Simplify by combining like terms.
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2h  3k  7(2h  3k)
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5x 2y
Chapter 1 Notes
Algebra II
Myrick
1.3 – Solving Equations
Definition: An ___________ is a mathematical statement that two expressions
are equivalent.
Definition: A number that makes the equation true is a ____________ of the
equation.
Example 1: Solve the equation. Check your solution.
6x  5  13
CHECK!
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Example 2: Solve the equation. Check your solution.
5(y  7)  25
CHECK!
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Example 3: Solve the equation. Check your solution.
6y  21  7  4y  20  5y
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CHECK!
Chapter 1 Notes
Algebra II
Myrick
Example 4: Solve the equation. Check your solution.
4(m  9)  3(m  4)
CHECK!
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1
Example 5: The formula for the area of a trapezoid is A  h(b1  b2 ) . Solve this
2
formula for b1.
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Chapter 1 Notes
Algebra II
Myrick
1.4 – Solving Inequalities
Definition: Just as we saw with equations, the ____________ of an inequality are
the numbers that make it true. The difference is that an inequality has many
solutions.
Note: Because there are multiple solutions, we often graph the solutions to
an inequality on a number line. When doing so, the following applies:

< and > should be graphed using an open circle.

 and  should be graphed using a closed circle.
Multiplying or Dividing by a Negative Number: When you multiply or divide by a
negative number when solving an inequality, you must _________ or ______ the
inequality sign.
Example 1: Solve the inequality. Graph the solution.
Example 2: Solve the inequality. Graph the solution.
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Chapter 1 Notes
Algebra II
Example 3: Solve the inequality. Graph the solution.
Example 4: Solve the inequality. Graph the solution.
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Chapter 1 Notes
Algebra II
Myrick
Definition: A ___________________________ is a pair of inequalities joined by
and or or.
Example 5: Graph the solution.
or
Example 6: Graph the solution.
4  2 x  6  22
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Chapter 1 Notes
Algebra II
Myrick
1.5 – Absolute Value Equations and Inequalities
Definition: The ___________________ of a number is its distance from zero on a
number line.
NOTE: Distance is always nonnegative.
If x > 0, then
. If x < 0, then
.
Solving Absolute Value Equations and Inequalities
1. Isolate the absolute value.
2. Rewrite the current equation or inequality into two separate equations.
a. For the first equation, simply get rid of your absolute value bars.
b. For the second equation, change the sign on each term not in the
absolute value bars. Then, get rid of the absolute value bars.
3. Solve each of the equations from step 2.
Example 1: Solve. Check your solutions.
CHECK!
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Chapter 1 Notes
Algebra II
Myrick
Example 2: Solve.
CHECK!
Definition: An ___________________________ is a solution of an equation
derived from the original equation but no actually a solution to the original
equation.
Example 3: Solve and check for extraneous solutions.
CHECK!
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Chapter 1 Notes
Algebra II
Example 4: Solve the absolute value inequality. Graph the solution.
2x  5  3
Example 5: Solve the absolute value inequality. Graph the solution.
 2 x  1  5  3
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Myrick