Download Solving a Division Equation

10/3/11
In your notebook, answer completely the
following:
Draw a picture of what an equation looks like to
you. Then use your picture to solve an
equation of your own.

Objective

solve one-step equations using algebra
Equationmathematical
sentence
with an equal sign
Like a scale,
both sides
must be balanced
Solving an Equation
How can you get the “unknown” by itself?
Addition and Subtraction Properties of Equality
Adding or subtracting both sides of the equation
by the same nonzero number produces an
EQUIVALENT EQUATION.
“Undo” the operation by using the INVERSE (opposite)
operation to both sides of the equation.
Solving Addition Equations…
Isolate the variable! Get ‘m’ by itself.
To get the ‘m’
by itself get rid of
“adding 24.”
m + 24 = -18
- 24 -24
Do the opposite.
“Subtract 24.”
Whatever you do to
one side of the equation
you must do the other side.
m = -42
Check Your Work!
m + 24 = -18
m = -42
(-42) + 24 = -18
Are both sides equal?
Try It Out
1). x + 7 = 4
1). (-3) + 7 = 4
2). 7 = 9 + h
2). 7 = 9 +(-2)
3). 13 = x + 7
3). 13 = (6) + 7
4). f – 0.4 = 3.1
4).(3.5) – 0.4 = 3.1
Solving Subtraction Equations…
Isolate the variable! Get ‘y’ by itself.
To get the ‘y’
by itself get rid of
“subtracting 15.”
Do the opposite.
“Add 15.”
-13 = y - 15
+15
+15
Whatever you do to
one side of the equation
you must do the other side.
2=y
Check Your Work!
-13 = y - 15
2=y
-13 = (2) - 15
Are both sides equal?
Try It Out
1). t - 7 = -3
1). (4) - 7 = -3
2). 6 = w - 3
2). 6 = (9) - 3
3). ¾ = r – 2½
3). ¾ = (3¼)– 2½
4). -1.5 = p - 7
4). -1.5 = (5.5) - 7
Solving an Equation
How can you get the “unknown” by itself?
Multiplication and Division Properties of Equality
Multiplying or dividing both sides of the equation
by the same nonzero number produces an
EQUIVALENT EQUATION.
“Undo” the operation by using the INVERSE (opposite)
operation to both sides of the equation.
Solving a Multiplication Equation
-2y = 28
-2
-2
y = -14
“Undo”
multiplication
by dividing
both sides of the
equation
Check Your Work!
-2y = 28
y = -14
-2(-14) = 28
Are both sides equal?
Try It Out
1). -7t = 63
1). -7(-9) = 63
2). -144 = 12d
2). -144 = 12(-12)
3). 10x = 5
3). 10(1/2) = 5
4). -1.5g = -7
4). -1.5(4.67)= -7
Solving a Division Equation
5· j = -7 · 5
5
j = -35
“Undo”
division by
multiplying
both
sides of the
equation
Check Your Work!
j = -7
5
-35 = -7
5
j = -35
Are both sides equal?
Try It Out

1). r ÷ 8 = -2
1). -16 ÷ 8 = -2

2). v = 8
4
2). 32 = 8
4
3). 9 = a
5
 4). e/-7= -2

3). 9 = 45
5
4). 14/-7 = -2
Find the width of the rectangle.
x
2
Area = 38 cm²
z=3
x = 19
9
z
Area = 27 m²
Solving a Two-Step Equation
How can you get the “unknown” by itself?
3x + 5 = -19
“Undo” operations by using the INVERSE (opposite)
operation to both sides of the equation.
Solving Two-Step Equations
STEP
STEP
STEP
STEP
1234-
“Undo” addition and/or subtraction.
“Undo” multiplication and/or division.
Solve for the variable.
Check your work.
Solving Two-Step Equations…
Isolate the variable! Get ‘x’ by itself.
To get the ‘x’ by
itself first get rid
of “adding 5.”
3x + 5 = -19
-5
-5
Do the opposite.
“Subtract 5.”
Whatever you do to
one side of the equation
you must do the other side.
To get the ‘x’ by
itself get rid
of “multiplying by 3.”
Do the opposite.
“Divide by 3.”
3x = -24
3
3
x = -8
Check Your Work!
3x + 5 = -19
x = -8
3(-8) + 5 = -19
Are both sides equal?