Transcript Introduction To Equation Solving.

Introduction To
Equation Solving.
x
x
Solve :
2x + 1 = 4
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Solving A Basic Equation.
Consider the equation below:
This can be represented by the
scales and marbles below. The
problem is to find out how many
marbles are in the box to make
the scales balance.
x + 2 = 5
(-2)
x
(-2)
=
3
The solution to the
equation is x = 3 .
That is to say that
there are three
marbles inside the
box to keep the
scales balanced.
x
Remove two marbles from each side.
Further Example.
Solve the equation :
m + 4 = 7
(-4)
Draw scales to represent the equation:
m
(-4)
m = 3
There are three
marbles in the box
to keep the scales
balanced. Hence :
m=3
How many marbles can we remove from
both sides?
4 marbles
What Goes In The Box ?
Solve the following equations:
(1) x + 8 = 14
x=6
(2) t + 10 = 18
(5) f + 14 = 34
f = 20
(6) b + 13 = 32
t=8
b = 19
(3) w + 3 = 12
w=9
(7) g + 70 = 110
g = 40
(4) h + 7 = 20
h = 13
(8) s + 27 = 74
s = 47
More Than One Box.
Draw scales to represent the equation:
Solve the equation:
3x = 9
3
x
x
x
x
3
=
3
There are three
marbles in each
box.
(1) If there are 9 marbles in three
boxes how many are in 1 box ?
3 marbles
What Goes In The Box ? 2
Solve the following equations:
(1) 2f = 10
f=5
(2) 3m = 12
m=4
(3) 4t = 12
t=3
(4) 6k = 24
k=4
(5) 5y = 45
y=9
(6) 9 d = 54
d=6
Further Example.
Solve the equation:
2x + 4 = 12
(-4)
Draw scales to represent the equation.
x
x
(-4)
2x
= 8
2
2
How many marbles can be removed
from both sides?
4
4 marbles
x
=
There are 4
marbles in each
box. Hence x = 4
is the solution.
If two boxes contain 8 marbles how
many marbles are in one box?
4 marbles
Solve the equation :
3x + 5 = 17
(-5)
3x
x
x x
= 12
3
x
(-5)
Draw scales to represent the equation:
3
=
4
As there are 4
marbles in
each box the
solution is
x=4
How many marbles can you remove from
both sides?
5 marbles.
If three boxes contain 12 marbles then how
many marbles are in one box ?
4 marbles
What Goes In The Box ? 3
Solve the equations below:
(1) 2h + 6 = 20
(5) 4r + 14 = 26
h=7
r=3
(2) 3n + 11 = 26
(6) 8f + 21 = 37
n=5
(3) 4w + 5 = 29
f=2
w=6
(7) 6a + 32 = 44
a=2
(4) 7t + 3 = 31
(8) 9p + 32 = 59
t=4
p=3
Solving Equations With Subtractions.
Solve the equation:
2y – 3 = 7
+3
y
y
+3
2y = 10
2
y
Draw scales to represent the equation:
2
= 5
There are 5
marbles in
each box.
y=5
The take away three means that three
marbles have fallen out of a box.
If you place the three fallen marbles
back in the box what must you do to the
other side of the balance ?
Add three marbles.
Now solve as before.
Further Example.
Solve the equation:
3m – 7 = 11
+7
m
m
m
+7
3m
= 18
3
3
m
Draw scales to represent the equation:
=
6
There are 6
marbles in
each box.
m=6
How many marbles must be added to each
side?
7 marbles.
Now solve as before.
What Goes In The Box ? 4.
Solve the equations below:
(1) 3n – 5 = 1
(5) 6d – 7 = 11
n=2
d=3
(2) 4f – 8 = 12
(6) 7r – 14 = 21
f=5
r=5
(3) 5h – 17 = 13
h=6
(7) 8v – 21 = 35
v=7
(4) 2k – 21 = 31
(8) 9p – 26 = 28
k = 26
p=6
More Complex Equations.
Draw scales to show the equation:
Solve the equation:
4m – 2 = m + 7
(+2)
m m m m
m
(+2)
4m = m + 9
(- m)
(- m)
How many marbles can you put back ?
2 marbles.
3m =
9
How many boxes can you remove ?
3
3
1 box.
m =
3
There are three marbles in each box .
Further Example.
Solve the equation:
Draw scales to show the equation:
6g – 3 = 2g + 9
+3
g
+3
6g
g
g
g
g
g
g
g
= 2g + 12
(-2g)
(-2g)
4g
= 12
4
4
How many marbles can we add to both sides ?
3 marbles.
How many boxes can you remove from both sides?
g
= 3
2 boxes
There are 3 marbles in each box.
What Goes In The Box 5 ?
Solve the equations below :
(1) 4 m – 3 = m + 15
m=6
(2) 6y – 2 = 2y + 18
y=5
(3) 6t + 3 = 3t + 15
t=4
(4) 8r – 7 = 3r + 23
r=6
(5) 10 w – 9 = 3w + 33
w=6
(6) 9f + 14 = 3f + 56
f=7