Download Equations - Lesson 1

What is an Equation
 An equation is an expression with an ‘equal’ sign
and another expression.
 EXAMPLE:
 x+5=4
 2x – 6 = 13
 There is a Left side, an equal sign, and a right
side.
Linear Equations
 A Linear Equation is a polynomial of
degree 1.
 That means that the exponent is a one.
 Example:
 x1 + 5 = 4
 2x1 – 6 = 13
QUADRATIC EQUATIONS
 A quadratic equation is a polynomial with a
degree 2.
 Which means that the exponent is a 2.
 Example:
 x2 - 3x – 10 = 5
 x2 - 25 = 2
Solving Equations
 In order to solve for the unknown variable, you
must isolate the variable using the zero effect.
 ZERO EFFECT: For every positive cancels out
every negative to equal zero.
 Example:
 - 4 + (+4) = 0
 17 + (-17) = 0
Solving Equations
 The goal to solve an equation is to get the
unknown variable by itself. That is isolate the
variable.
 To do this, you must think of an equation like a
balance scale.
 You must keep the equation balanced at all times.
 Therefore, whatever mathematical
operation you perform to the left side,
you must perform the same operation to
the right side.
EXAMPLE 1
x – 4 = 10
We can see from
observation that the answer
is 14, because 14 – 4 = 10
STEPS:
1. Isolate variable
x – 4 + 4 = 10 + 4
x – 4 + 4 = 10 + 4
x = 14
Added +4 to both sides to stay balanced
Zero effect isolated the variable x
x–3=4
x – 17 = 3
x+5=8
x–3+3=4+3
x – 17 + 17 = 3 + 17
x+5-5=8-5
x–3+3=4+3
x – 17 + 17 = 3 + 17
x+5–5 =8-5
x=7
Added +3 to
both sides to
cause the
zero effect
which isolated
the variable
x = 20
x=3
Check:
Check:
x – 17 = 3
x+5=8
(20) – 17 = 3
(3) + 5 = 8
3=3
8=8
Two Step Solutions
 Step 1 – Isolate variable using zero effect.
 Step 2 – Make variable worth one whole.
 If variable is greater than 1, you would
divide by the number in front of the
variable to make it worth one whole.
Solve: 2x – 4 = 10
Remember that
whatever you do to
one side, do to the
other
Solution:
2x – 4 + 4 = 10 + 4
Add + 4 to both sides to
isolate the variable
2x = 14
2x = 14
2
2
x=7
Divide by the number in
front of the variable to
make variable worth one
whole.
Solve: 3x – 3 = 4
Remember that
whatever you do to
one side, do to the
other
Solution:
3x – 3 + 3 = 4 + 3
Add + 3 to both sides to
isolate the variable
3x = 7
3x = 7
3
3
x= 7
3
Divide by the number in
front of the variable to
make variable worth one
whole.
Solve: 5x – 17 = 3
Remember that
whatever you do to
one side, do to the
other
Solution:
5x – 17 + 17 = 3 + 17
Add + 17 to both sides to
isolate the variable
5x = 20
5x = 20
5
5
x=4
Divide by the number in
front of the variable to
make variable worth one
whole.
Solve: 10y + 5 = 8
Remember that
whatever you do to
one side, do to the
other
Solution:
10y + 5 - 5 = 8 - 5
Subtract 5 from both sides
to isolate the variable
10y = 3
10y = 3
10 10
x=
3
10
Divide by the number in
front of the variable to
make variable worth one
whole.
Two Step Solutions
 Step 1 – Isolate variable using zero effect.
 Step 2 – Make variable worth one whole.
 If variable is less than 1(fraction), you would
multiply by the denominator, to make the
variable worth one whole.
Solve: x
4
= 3
Remember that
whatever you do to
one side, do to the
other
Solution:
x
4
4
()
= 4(3)
x
= 12
4
4
()
x = 12
Multiplied by the
denominator to make the
variable worth one whole.
Solve: x
3
+ 4 = 10
Remember that
whatever you do to
one side, do to the
other
Solution:
x
+ 4 – 4 = 10 - 4
3
x
3
3 = 3(6)
x
3
3 = 18
()
()
x = 18
Subtract 4 from both sides
to isolate the variable
Multiplied by the
denominator to make the
variable worth one whole.
Solve: x
4
= 1
2
Remember that
whatever you do to
one side, do to the
other
Solution:
x
4
4
1
2
() ( )
= 4
x
= 2
4
4
()
x=2
Multiplied by the
denominator to make the
variable worth one whole.
Class work
 Make notes
 Complete questions #1-4 on Lesson 1
worksheet