Solving Equations
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Transcript Solving Equations
Solving Equations
Foundation Tier GCSE
Starter Activity – Evaluate when…...
Put the cards in order of smallest on the
left to largest on the right….when….
x = 10
x=1
x=3
x = -5 ( hard!!)
Aims for today’s lesson
To understand what an equation is….
To be able to make an equation…..
To know what solving an equation
means, and be able to solve simple
equations
What is an Equation?
An equation looks a bit like the algebra we
were doing in earlier lessons……
The key difference is suggested by the word
itself……
EQUALS
TIONS
An equation always has an equals sign
somewhere (usually in the middle of the
problem).
How to make an Equation…
OK – think of a number…….
Double your number…..
Subtract (take off) 3….
You get the answer 9. What was the
original number you thought of?
How to make an Equation…
OK – think of a number……. Call it x
Double your number………..that’s 2x
Subtract (take off) 3……….so 2x - 3
You get the answer 9…..so 2x – 3 = 9
What was the original number you thought
of?
Reverse the steps….start with the 9 …. Now
add 3….that’s 12…..divide by 2….so my
original number, x = 6. I now know what x is
– which means I’ve solved my equation!!
How to make an Equation…
OK – think of a number…………x
multiply your number by 5…….that’s 5x
add 2……………now that gives 5x + 2
You get the answer 22…..so that’s 5x+2=22
Now to solve it…..start with the 22 …
..subtract the 2….that’s 20….divide by 5 …
..so x=4
Solving Equations….
Example: Solve
3x + 4 = 25
Method: write the equation down:
Notice how an
3x + 4 = 25
equation is like a
Subtract 4 from the equation…..
3x + 4 – 4 = 25 – 4
3x = 21
balance – what you
do to one side of
the equals, you
must also do on the
other side…..
Divide the equation by 3…….
x=7
(Check!!)
Now for the
HUMAN
EQUATION!!
Solve 4x + 6 = 20
Solving Equations….2
Example: Solve
7x - 5 = 30
Method: write the equation down:
Again –
7x - 5 = 30
Add 5 to both parts of the equation…. the
equation
7x - 5 + 5 = 30 + 5 is a
7x = 35
balancing
act….
Divide the equation by 7…….
x=5
(Check!!)
Solving Equations….3
Example: Solve
8x + 1 = 13
Method: write the equation down:
Here we do the
8x + 1 = 13
same thing to
Subtract 1 from both parts of the equation….
both sides –
8x + 1 - 1 = 13 - 1 but try to
isolate the x
8x = 12
term…
Divide the equation by 8…….
x = 1.5 (Check!!)
Equations on the web…..
Use 11-14, Equations, level 2
Review today’s lesson
To understand what an equation is….
To be able to make an equation…..
To know what solving an equation
means, and be able to solve simple
equations
Try this algebra pyramid
What is x to
make this work?
2x
24
5
8
Aims for today’s lesson
1.
2.
To know what solving an equation
means, and be able to solve simple
equations with only one x term
To understand how to solve
equations with an x term on each
side (grade C +)
Solving Equations….
Example: Solve
2x + 14 = 25
Method: write the equation down:
Notice how an
2x + 14 = 25
equation is like a
Subtract 14 from the equation…..
balance – what you
do to one side of
the equals, you
must also do on the
other side…..
2x + 14 – 14 = 25 – 14
2x = 11
Divide the equation by 2…….
x = 5.5 (Check!!)
Try these quickly…..
Solve:
1.
2.
3.
4.
5.
3x + 6 = 15
4x – 3 = 13
5x + 2 = 27
23 + 3x = 44
50 = 26 + 8x
Solving Equations with TWO x terms
Example: Solve 3x + 4 = 2x + 9
Method: write the equation: 3x + 4 = 2x + 9
Subtract 4 from the equation…..
3x + 4 – 4 = 2x + 9 – 4
3x = 2x + 5
Now subtract 2x from the equation …….
3x – 2x = 2x – 2x + 5
x = 5 (Check!!)
Solving Equations with TWO x terms
Example: Solve 5x - 6 = 3x + 8
Method: write the equation: 5x - 6 = 3x + 8
Add 6 to both sides of the equation…..
5x - 6 + 6 = 3x + 8 + 6
5x = 3x + 14
Now subtract 3x from both sides …….
5x – 3x = 3x – 3x + 14
Now 2x = 14
so x = 7
Solving Equations with TWO x terms
Example: Solve x - 6 = 5x + 10
Method: Swap the equation: 5x + 10 = x – 6
Subtract 10 from both sides of the equation…..
5x + 10 – 10 = x – 6 – 10
5x = x – 16
Now subtract x from both sides …….
5x – x = x – x – 16
Now 4x = - 16
so x = - 4
Equations on the web…..
Use 11-14, Equations, level 4
These were the aims for today’s
lesson:
To know what solving an equation
means, and be able to solve simple
equations with only one x term
2. To understand how to solve equations
with an x term on each side (grade C +)
Now check your learning by having a go at
this question from a GCSE paper:
1.
Solve the equation x – 4 = 3(x + 1).
......................................................................................
......................................................................................
......................................................................................
......................................................................................
......................................................................................
......................................................................................
Answer x = ................................................... (3 marks)
Aims for today’s lesson
1.
2.
To understand how to solve
equations involving a divide and an
x term (grade C )
To know how to deal with brackets
in the equation (grade C)
Dealing with fractions…..
Solve: x = 10
3
Now begin by looking carefully at what the equation is
actually saying:
“ x divided by 3 equals 10” or….
“ what number, divided by 3, is 10?”
The answer is obviously x = 30
– so it seems all you
need to do is let the 10 be multiplied by the 3…..In
fact, this must be right, because the opposite of divide
by 3 is multiply by 3…..
x = 30
Dealing with fractions 2
Solve: x = 4
5
Again, what the equation is actually saying is:
“ x divided by 5 equals 4” or….
“ what number, divided by 5, is 4?”
The answer is obviously x = 20
– so again all you
need to do is let the 4 be multiplied by the 5…..this
must be right, because the opposite of divide by 5 is
multiply by 5…..
x = 20
Dealing with fractions 3
Solve: x + 6 = 10
2
First, take 6 from both sides…..gives you….
x = 4
2
Now multiply both sides by 2…..giving:
x = 8
Dealing with fractions 4
Solve: 2x - 4 = 6
7
First, add 4 to both sides…..gives you….
2x = 10
7
Now multiply both sides by 7…..giving:
2x = 70
Finally divide both sides by 2, giving….
x = 35
These were the aims for today’s
lesson:
To understand how to solve equations
involving a divide and an x term (grade
C +)
2. To know how to deal with brackets in
the equation (grade C+)
Now check your learning by having a go at
this question from a GCSE paper:
1.
Solve these equations.
(a) 3p 5 = 7
.....................................................................................................................................
Answer p = .................................................................................................................
q
(b) 3 = 4
.....................................................................................................................................
Answer q = .................................................................................................................
(c) 2(x + 3) = 11
.....................................................................................................................................
Answer x = .................................................................................................................
(d) 4y+7= 2 y
.....................................................................................................................................
Answer y= ............................................................................................................ .......