Equations vs. Expressions different
Alarge part of algebra involves expressions and
equations; these are objects
manipulating
and a clear distinction between them is necessary.
EQUATIONS
EXPRESSIONS
What are they?
one
Expressions express a value using Equations are statements that say
value as
variables and constants, e.g. 3x-5. expression must be the same in
another expression. e.g. 3x -5= x.
Acalculation, e.g. "three times a number
then decrease by five", Statements canbe true or false (or always
true or always false) depending on the
value of the variable.
e.g. 3x = 12 or 6 =6 or 3 = 4.
What do they look like?
Expressions do not contain an = sign. Equations contain an = sign.
There is no "other side".
There are two sides, with one expression on
each side.
What is done with them?
e
Expressions are simplified to different Equations are solved (by simplifying the
looking forms that have the same algebraic expressions on either side).
meaning (or value).
Asolution to an equation is a number that
e.g. X +3x has the same meaning as 4x
makes the statement true when it is
does, but they have different forms.
substituted into the variables on both sides.
Expressions are simplified (and cannot be e.g. 4 is a solution to the
solved). statement 3x = 12
because on the left hand side (LHS) we get
avalue of 12,
which is the same as the
Expressions can only be "equal to a value of the RHS.
number" if al the variables have been
substituted for constants, and the
calculation is carried out. Solving an equation means to find
solutions. any/all
e.g. if x is replaced with 3 in the
4x, then the expression will haveexpression
a value of
12 (the "answer after
into 4x is 12). substituting x = 3
Gr.9
, Solving Equations by Inspection
solution(s) by substituting vour answerle)
Solve the following equations by inspection, and check your
separately.
into the LHSand RHS linear.
are
ldentify which of theequations
n+10 = 7 nz n 3
12c =-144 C=- 2
ii.
ii. 2.x =3
3
iv. 12y = -3y
solution)
V. h= 25 (there is more than one
h
vi. p=p(there is more th¡n one solution)
P=I
vi. 2-2* = 32
Operations
Solving LINEAR Equations Using Inverse
Additive and Multiplicative Inverse Operations
gives us the tools to isolate
Many equations are too complicated to solve by inspection, but algebra
a number".
the variable by reducing the equation to a simple statement "the variable eguals
We have seen that to solve an equation means to get the variable on its own on one side of the
equation. To get the variable by itself we need to use inverse operations.
Operation Inverse Operation
IX +
X
X
* Note that powers (exponents) have
special rules
Equations with exponents greater than 1 are NOT(when solving equations).
LINEAR equations.
Gr.9
Unit 8
Alarge part of algebra involves expressions and
equations; these are objects
manipulating
and a clear distinction between them is necessary.
EQUATIONS
EXPRESSIONS
What are they?
one
Expressions express a value using Equations are statements that say
value as
variables and constants, e.g. 3x-5. expression must be the same in
another expression. e.g. 3x -5= x.
Acalculation, e.g. "three times a number
then decrease by five", Statements canbe true or false (or always
true or always false) depending on the
value of the variable.
e.g. 3x = 12 or 6 =6 or 3 = 4.
What do they look like?
Expressions do not contain an = sign. Equations contain an = sign.
There is no "other side".
There are two sides, with one expression on
each side.
What is done with them?
e
Expressions are simplified to different Equations are solved (by simplifying the
looking forms that have the same algebraic expressions on either side).
meaning (or value).
Asolution to an equation is a number that
e.g. X +3x has the same meaning as 4x
makes the statement true when it is
does, but they have different forms.
substituted into the variables on both sides.
Expressions are simplified (and cannot be e.g. 4 is a solution to the
solved). statement 3x = 12
because on the left hand side (LHS) we get
avalue of 12,
which is the same as the
Expressions can only be "equal to a value of the RHS.
number" if al the variables have been
substituted for constants, and the
calculation is carried out. Solving an equation means to find
solutions. any/all
e.g. if x is replaced with 3 in the
4x, then the expression will haveexpression
a value of
12 (the "answer after
into 4x is 12). substituting x = 3
Gr.9
, Solving Equations by Inspection
solution(s) by substituting vour answerle)
Solve the following equations by inspection, and check your
separately.
into the LHSand RHS linear.
are
ldentify which of theequations
n+10 = 7 nz n 3
12c =-144 C=- 2
ii.
ii. 2.x =3
3
iv. 12y = -3y
solution)
V. h= 25 (there is more than one
h
vi. p=p(there is more th¡n one solution)
P=I
vi. 2-2* = 32
Operations
Solving LINEAR Equations Using Inverse
Additive and Multiplicative Inverse Operations
gives us the tools to isolate
Many equations are too complicated to solve by inspection, but algebra
a number".
the variable by reducing the equation to a simple statement "the variable eguals
We have seen that to solve an equation means to get the variable on its own on one side of the
equation. To get the variable by itself we need to use inverse operations.
Operation Inverse Operation
IX +
X
X
* Note that powers (exponents) have
special rules
Equations with exponents greater than 1 are NOT(when solving equations).
LINEAR equations.
Gr.9
Unit 8
