Download Solving One-Step Equations

Solving OneStep Equations
S.W.B.A.T
 Students
will be able to take their
knowledge of order of operations and
substitution to solve a one step equation
Do Now:
 Answer
leaf

the following on a piece of lose
a= 5 and b= 2
 8a
÷b
Solving Equations
 In
an equation, the variable represents
the number that satisfies the equation
 To solve an equation means to find the
value of the variable that makes the
equation true
Process of Solving an Equation
 The
process of solving an equation
involves isolating the variable, making it
have a coefficient of 1, on one side of the
equation
Addition property of equality
 If
an equation is true and the same
number is added to each side of the
equation, the resulting equivalent
equation is also true
 For any real numbers a, b and c, if a=b,
then a + c = b + c
Examples
 Solve





by adding
C – 22 + 54
Since we are subtracting 22 from c, we
must add 22 to get c by itself.
What we do to the left side we must do to
the right side
C – 22 + 22 = 54 + 22
C = 76
 This
is the horizontal method, I will show you
the vertical method on the board
Check
C
C
= 76
– 22 = 54
 76 – 22 = 54
 54 = 54
Subtraction Property of
Equality
 If
an equation is true and the same
number is subtracted from each side of
the equation, the resulting equivalent
equation is also true
 For any real numbers a, b and c, if a = b,
then a – c = b - c
Examples
 Solve
by subtracting
 63 + m = 79
 63 is being added to m, in order to isolate
the variable we must subtract 63 from
each side
 63 – 63 + m = 79 – 63
 M = 16
Check
m
= 16
 63 + m = 79
 63 + 16 = 79
 79 = 79
Multiplication Property of
Equality
 If
an equation is true and each side is
multiplied by the same nonzero number,
the resulting equation is equivalent
 For any real numbers a, b and c, if a = b,
then ac = bc
Examples


Solve by
multiplying
Take the
fraction
being
multiplied
by the
variable
and multiply
each side
by its
reciprocal
2
1
q=
3
2
3 2
3 1
( )q = ( )
2 3
2 2
3
q=
4
Division Property of Equality
 If
an equation is true and each side is
divided by the same nonzero number, the
resulting equation is equivalent
 For any real numbers a, b and c, if a = b,
then
a b
=
c c
Examples
 Solve
by dividing
 39 = -3r
 Since we want r is being multiplied by -3
and we want r to be by itself we must
divide each side by -3
 39 = -3r
------- -----3
-3
-13 = r
Check
 -13
=r
 39 = -3r
 39 = -3 ( -13)
 39 = 39