Transcript Equations

Expressions and Equations
Vocabulary
• Variable - a letter that is used to
represent an unknown number
• Coefficient - A constant (number) that is
in front of a variable (Ex: 4 is the
coefficient in 4x)
• Expression - A collection of constants,
variables, and operations - NO EQUAL
SIGN (Ex: 3x + 2)
Vocabulary continued
• Term - The individual parts of an
expression (Ex: 4x and 2 in 4x+2)
• Equation - shows that two or more
expressions are equal (Ex: 4x - 2 = 6)
• Inequality - shows that two or more
expressions are NOT equal by using >,
<, ≤, or ≥ (Ex: 2x + 1 > 5)
Writing Expressions
• Phrases can be turned into algebraic
expressions by looking for clue words
• Ex: the total of 5 and c will be written as
5+c
• Ex: the product of k and 9 will be written
9k (when being multiplied the number
always comes before the variable)
Clue words
• Addition: add, sum, plus, more than,
total, all together
• Subtraction: minus, take away, less,
less than, difference, decrease
• Multiplication: times, product, twice
• Division: quotient, divided into, divided
by, out of
Writing Equations
• Equations are different from
expressions because they contain an
equal sign
• Ex: A number increased by 7 is 11
would be written: x + 7 = 11
Writing Equations
• Break the sentence into parts to turn it
into an algebraic equation:
Ex: Four less than three times a number is
fourteen
Four less than means - 4
Three times a number means 3n
Is fourteen means =14
So 3n - 4 = 14
Solving equations
• Equations must stay balanced.
• To solve an equation, you must get the
variable alone on one side of the equal
sign. To do this, you must get rid of any
other numbers by performing the
opposite function. BUT whatever you do
to one side, you must do to the other.
Solving Equations
• X+3=6
• We need to get x by itself so we get rid
of 3 by subtracting (opposite of addition)
- BUT what we do to one side we must
do to the other
• X+3-3=6-3
• This leaves x = 3
Solving Equations
• Ex: n - 7 = 3
• We want the n by itself so we have to
get rid of the 7 so we add (opposite of
subtraction) 7 BUT what we do to one
side we must do to the other
• N-7+7=3+7
• N = 10
Solving equations
• EX: 3n = 12
• We want n by itself so we must get rid
of the 3. 3n means 3 times n so we
have to do the opposite function divide. BUT what we do to one side, we
must do to the other
• 3n ÷ 3 = 12 ÷ 3
• N=4
Solving equations
• Ex: n ⁄ 4 = 5
• We have to get n by itself. N and 4 are
divided so we do the opposite - multiply
BUT what we do to one side we must
do to the other.
• N⁄4x4=5x4
• N = 20