chapter 1: expressions, equations and inequalities 1, i, iii, iii... · mathb65 ch 1 i,ii,iii, iv...
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MathB65 Ch 1 I,II,III, IV .notebook
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Chapter 1: Expressions, Equations and InequalitiesI. Variables & Constants
II. Algebraic Expressions
III. Translations
IV. Introduction to Equations
V. The Additive/Multiplication Principles
VI. Strategy to Solving Linear Equations of 1-Variable
VII. Formulas
VIII. Problem Solving using Algebra
IX. Intervals
X. Solving Inequalities
XI. Intersections, Unions, & Compound Inequalities
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Definition: A variable is a quantity which can vary or change.
Exercise:
1) Let T represent be the temperature in degrees Fahrenheit. What does T = -15
mean in this case?
2) Let t be the number of years since 1995. What does t = 10 mean in this
situation?
I. Variables & Constants
Don't forget "units"
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Definition: A constant is a quantity which does not vary or change.
Exercise: A rectangle has a given area of 24 square inches.
1) Give three possible rectangles.
2) What is the constant in this exercise?
3) What are the variables in this exercise?
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II. Algebraic ExpressionsDefinition:An algebraic expression consists of variables and/or numerals often with operation signs and grouping symbols.
Exercise: The cost to take a particular taxi company in New York City is
given by the expression 3 + 2x, where x is the number of miles driven.
1) What is the cost to take a taxi ride for 8 miles?
2) What does the 2x mean in the expression?
3) What does the 3 mean in the expression?
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Exercise: Find the numerical value for the expressions given
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Combining Like Terms
When two terms have variable factors that are exactly the
same, the terms are called like or .
respective powers are
identical.
Match the like terms
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Exercise: Simplify
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The Distributive Law: a(b + c) = ab + ac
Show that
Use distributive law to re-write the following expressions.
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III. TranslationsIdentify the following key words with one of the symbols
Addition
Subtraction
Multiplication
Division
Minus
Quotient of
Added to
Ratio of
Product of
Increased by
Decreased by
Of
Divided by
Sum of
Subtracted from
Multiplied by
Divided into
More than
Less than
Per
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1) 5 more than 20
2) 5 less than 20.
3) The difference of 6 and 10.
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Translate each phrase to an algebraic expression.
1) 9 more than y. 2) 7 less than x.
3) The difference of 7 and x. 4) The product of 3 and twice t.
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5) The sum of three times a number and 7.
6) Three times the sum of a number and 7.
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IV. Introduction to EquationsAn equation you should know!
Find the area of a triangle where the base is 12 inches and height is 7.2 inches.
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When two algebraic expressions have an equal symbol, =, between them, then the sentence is an
Question:Which of the following is an equations and which is an expression?
x + 12 = 21
What if we
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Definition: of an equation is a replacement of the variable(s) that make the equation true.
Question: is 4 a solution of x + 12 = 21?
Question: is 9 a solution of x + 12 = 21?
Definition: solve an equation means to find all of its solutions.
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Exercise: Determine if the given number is a solution to the equation.
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Translate the problem into an equation.
1) What number increased by 5 is 120?
2) When we take twice a number, the result is 50.
3) The differenct of a number and five is the same as twice the number.
Words that translate into equality (=):
"Is the same as""The result is"
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Chapter 1 HomeworkPart I: Variables & Constants
1) Let n be the number (in thousands) registered at Bakersfield College. What
does n = 12 mean in this situation?
2) Let c be the cost (in dollars) to mail a package from the post office. What
does c = 5.62 mean in this situation?
3) The perimeter of a rectangle is the sum of all its four sides. A particular
rectangle has a fixed perimeter of 100 feet.
a) Give two different rectangles that fit this description.
b) What are the variables in this situation?
c) What are the constants in this situation?
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Part II: Algebraic Expressions
Evaluate the given expression for
the given value of the variable.
Simplify each algebraic
expression.
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Part III: Translations
Write the following as a algebraic
expression.
15) The sum of five and a number
16) The product of a number and 10
17) The difference of 10 and a
number
Part IV: Introduction to Equations
Determine if the given number is a
solution to the equation.
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