Solving Equations Student Notes - MS. FORD'S MATH CLASS
Transcript of Solving Equations Student Notes - MS. FORD'S MATH CLASS
● Variable: a letter which represents an unknown number (any letter can be used as a variable)
a x y z r v d
● Coefficient: the number in front of (touching) a variables (implies multiplication)
3c -15x𝟐
𝟑𝐤
● Constant: a number
5 8 -12 6.25 𝟓
𝟖
● Operation:+ ÷ − ×
Important Vocabulary
● Expression: a mathematical phrase made up of variables and/or constants and operations
𝟑𝒙 + 𝟓● Equation: a sentence that states that two
mathematical expressions are equal.
−𝟐𝒈 − 𝟗 = 𝟏𝟓● Inequality: a sentence that states that two
mathematical expressions are not equal.
𝟏𝟐 + 𝟓𝒚 < −𝟏𝟎
Important Vocabulary
● Term: when addition or subtractions signs separate an algebraic expression, each part is a term
𝟑𝒙 + 𝟒𝒚 − 𝟖
● Inverse: opposite
● Isolate: to be alone
Important Vocabulary
Term 1 Term 2 Term 3
What’s the point!?
We want to know the value of the unknown number.
In order to do so, we have to ISOLATEthe variable using INVERSE operations.
2x + 8 = 12
The inverse of adding 8 is subtracting 8
*Whatever you do to one side of the equation you must also do to the other side to keep it balanced!!
+8 and -8 cancel each other out (they make 0)
Draw a line at the equal sign to divide your equation into 2 parts.
2x =4
The inverse of multiplying by 2 is dividing by 2
Dividing 2x by 2 leaves 1 x (the variable is now isolated!)
*Whatever you do to one side of the equation you must also do to the other side to keep it balanced!!
5x - 7 = -x + 35
The inverse of subtracting 7 is adding 7
*Whatever you do to one side of the equation you must also do to the other side to keep it balanced!!
-7 and +7 cancel each other out (they make 0)
Draw a line at the equal sign to divide your equation into 2 parts.
5x = -x + 42
The inverse of subtracting x is adding x
*Whatever you do to one side of the equation you must also do to the other side to keep it balanced!!
-x and +x cancel each other out (they make 0)
The inverse of multiplying by 6 is dividing by 6
Dividing 6x by 6 leaves 1 x (the variable is now isolated!)
*Whatever you do to one side of the equation you must also do to the other side to keep it balanced!!
● Like Terms: terms that have the same variables raised to the same exponent (or power), but have different coefficients
● Distributive Property: the process of distributing the number on the outside of the parentheses to each term on the inside.
Important Vocabulary
Like terms because each term consists of a single variable, x, and a numeric coefficient:
2x, 45x, x, 0x, -26x, -x
Like terms because they are all constants:
15, -2, 27, 9043, 0.6
Like terms because they are all y² with a coefficient: 3y², y², -y², 26y²
What are unlike terms?
The following two terms both have a single variable, but the terms are not alike since different variables are used: 17x, 17z
Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15y, 19y², 31y5
Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19x, 14xy
5 apples + 3 oranges
Distribute by multiplication:
15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is
simplified because we do not know what the value of n is at this time and cannot
complete the multiplication part of this problem.
)43(5 n )3(5 n
)4(5
n15 20
The Distributive Property
Expressions with variables:
Simplify 5(3n + 4).
No symbol between the 5 and the parenthesis indicates a multiplication problem.
Solve: 2x + 6(x + 1)
Explain how each of the below answers are wrong and why.
2x + 6x + 1
9x
Think – Pair – Share