### About Variable Definition:

A variable is a letter that is used to represent an unknown quantity. A term is a single number, variable, or the product of a number and one or many variables. Lastly, an algebraic expression is a single term, or a number of terms separated by "+" and/or "-" symbols.

Test Objectives

- Demonstrate the ability to evaluate an algebraic expression for given values
- Demonstrate the ability to determine if two or more terms represent "like terms"
- Demonstrate the ability to simplify an algebraic expression by combining like terms

#1:

Instructions: Evaluate each algebraic expression for the given value(s) of the variable(s).

a) -7x - 3 for x = 2

b) -7x - 3 for x = -2

c) -7x - 3 for x = 5

d) 10x^{2} + 7x - 1 for x = 2

e) 10x^{2} + 7x - 1 for x = -2

f) 10x^{2} + 7x - 1 for x = 5

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#2:

Instructions: Evaluate each algebraic expression for the given value(s) of the variable(s).

a) -9x^{3} - 6y for x = 1, y = 3

b) -9x^{3} - 6y for x = 2, y = -5

c) 2z^{2} - 5x - y for x = 3, z = 2, y = 7

d) 2z^{2} - 5x - y for x = -1, z = 5, y = -4

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#3:

Instructions: Determine if each are like terms.

a) 4x, -13x

b) 12yz, 7xz

c) 9ab, -4ba

d) -3y^{2}x, 15xy^{2}

e) 10z^{2}x^{4}a^{3}, -5a^{2}x^{4}z^{3}

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#4:

Instructions: Simplify.

a) 3(t - 4) + 7(x + 4)

b) 6(z - 6) + 3(z - 7) + 5

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#5:

Instructions: Simplify.

a) 3(2y - 9) + 7(z^{2} - y)

b) -2(-3x + 4) - (5x - 7) - 10

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Written Solutions:

#1:

Solutions:

a) -17

b) 11

c) -38

d) 53

e) 25

f) 284

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#2:

Solutions:

a) -27

b) -42

c) -14

d) 59

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#3:

Solutions:

a) like terms

b) not like terms

c) like terms

d) like terms

e) not like terms

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#4:

Solutions:

a) 3t + 7x + 16

b) 9z - 52

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#5:

Solutions:

a) 7z^{2} - y - 27

b) x - 11