Download Additive Opposite Algebraic Expression

Chapter R
Algebra Reference
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Additive Opposite
-a is the additive opposite of a
a + -a = 0
Examples:
-1 is the additive opposite of 1, so
-1 + 1 = 0
-(-1) is the additive opposite of -1, so
-(-1) + -1 = 0
so -(-1) = 1
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Algebraic Expression
An algebraic expression involves only the basic
operations of addition, subtraction, multiplication, or
division (except by 0), or raising to powers or taking
roots on any collection of variables and numbers.
4 x − 7,
m + 3,
and
xy 3 z
k
Algebraic expressions
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Terms
Equation
When taking a sum or difference of algebraic
expressions, each expressions is called a term.
In the expression
An equation is a statement that two
algebraic expressions are equal. A linear
equation in one variable involves only real
numbers and one variable.
2x + 3y – 4,
2x, 3y, and 4 are terms.
4 x − 7 = 8 and 5k + 3 = k + 1
Linear equations in one variable
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Example (one variable)
Terminology
A linear equation in one variable is also called a firstdegree equation.
If the variable in an equation is replaced by a real
number that makes the statement of the equation true,
then that number is a solution of the equation. An
equation is solved by finding its solution set, the set
of all answers.
Equivalent equations are equations with the same
solution set.
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Example:
If
x + 7 = 15,
then, by subtraction 7 from both sides of the
equation, we find:
x + 7 = 15
– 7 –7
x
= 8
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Example: Combining Principles
If
When combining principles, always isolate the
terms involving the variable first.
2x = 16,
then
Solve for z:
2x 16
= ,
2 2
so
2z – 3 = 7
x = 8.
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Combining like terms
Example
Like terms can be added by adding the constant part,
keeping the variable part.
5x + 3x = 8x
Solve for y:
2y + 15 = –y
Solution:
2 y + 15 = − y
− 2y
1
1
y− y = y
2
2
15 − 3 y
=
−3 −3
−5 = y
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− 2y
Example: Solving for a Specified
Variable
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Inequalities
Solve the formula 10 = 2L + 2W for L.
Solution
10 = 2L + 2W
-2W
-2W
10 – 2W = 2L
Subtract 2W.
10 − 2W 2 L
Divide by 2.
=
2
2
10 − 2W
= L or 5 − W = L
Simplify.
2
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Properties of Inequalities
If a < b, then a + c < b + c
If a < b and c > 0, then ac < bc
If a < b and c < 0, then ac > bc
Multiplying or dividing by a negative flips the
inequality.
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Exponent Terminolgy
a2 is read “a squared”.
a3 is read “a cubed”.
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