Evaluating Expressions

Remember from class we discussed the difference between numerical expressions and algebraic expressions.  Algebraic expressions contain a variable.  Also remember that expressions are part of equations.  An equation is demonstrating two expressions that are equal.  For example the equation y + 6 = x + 5 has two algebraic expressions which you know are equivalent given the equal sign.

To evaluate algebraic expressions you must know the value of the variable.  The values of the variables will always be given.  Here's an example:

Evaluate the expression 4b + 3c - 10 for b=5 and c=2.

To evaluate simply substitute the value of the variable and follow order of operations.  In class, I expect to see the substitution.  This is the expectation:

4(5) + 3(2) - 10   This shows the substitution
20 + 6 - 10          This demonstrates following the orders of operations
26 - 10
16                         Solution

Here's another

Evaluate  x^y - xyz + 6(z - y) when x=2, y=3, and z=(-1)

2^3 - (2)(3)(-1) + 6(-1 - 3)
8 - (-6) + 6(-4)
8 + 6 + (-24)
14 + (-24)
(-10)

Combining Like Terms

Writing Algebraic Expressions From Word Phrases

This can be challenging, however it is important to take your time and make sense of the problem.  Unfortunately there are no hard and fast rules (like integers) to interpret the word phrases into algebraic expressions, so we need to practice.  One of the harder phrases involve subtraction.  Look at the list below and be sure to study these phrases.

• A number less 9.........................n - 9
• A number less than 9.................9 - n
• A number is less than 9..............n < 9