Transcript File - PROJECT MATHS REVISION

INTRODUCING INEQUALITIES
Solve x  1  3
1 4x
Solve 1  x 
5
Remember : An Equation behaves like a Balance.
The Left Hand Side of the equals is one side of the scales.
The Right Hand Side of the equals is the other side.
A BALANCED EQUATION
Add +1 to both sides
STILL BALANCED
Now add -3 to both sides
STILL BALANCED
10  10
10  1  10  1
11  11
11  3  11  3
88
Solve x  1  3
What if the equals was replaced by a GREATER THAN sign (>)?
Or a LESS THAN sign (<) ?
Solve x  1  3
THE GOLDEN RULES STILL APPLY
Solve for x means get x on its own on one
side of the equation
What you do to the LHS you do to the RHS
Solve:
x is not on its own.
x 1  3
x 1  3
What’s blocking us? It’s +1
So Add -1 to both sides
x must be greater than 2
(As expected!)
Let’s Check
Pick a number
greater than 2.
Say 5
1 1
x2
x 1  3
5x  1  3
63
Are there any other numbers greater than 2 ?
Correct!
x 1  3
Try x=4
Try x=3
Try x=2
Try x=1
4 1  3  5  3
3 1  3  4  3
2 1  3  3  3
11  3  2  3
true
true
false
false
Which numbers greater than 2 to choose?
Anything even slightly greater than 2 will make
this inequality TRUE
NO
6
1.5
1
x 1  3
YES
1.857
2.143
2.5
10
5
1.8 1.99 2.01 2.2
Which numbers greater than 2 to choose?
x2
3 sets of Numbers that x can be an element of :
Natural Numbers (N)
Finger Counting
..  1, 0, 1 ..
Integers (Z)
Real Numbers (R)
Any number you
can put into this!
Show the solution set to x  2 on number lines.
x2
   
x N
0
x2
x2
x Z
x R
1
2
3
4
5
 x  {3, 4,5, 6,....}
0
1
2
3
4
5
6
Show the solution set to x  2 on number lines.
x2
    
x N
0
x2
x2
x Z
x R
1
2
3
4
5
6
 x  {2,3, 4,5, 6,....}
0
1

2
3
4
5
Show the solution set to x  2 on number lines.
x2
x2
x N
x Z
YOU TRY THEM
x2
x R
  
1 0
1
2
3
4
3
4
   
1 0
1
2
 x  {2,1, 0, 1,....}
1 0
1

2
3
4
2 Really Good Websites
http://www.onlinemathlearning.com/algebra-inequalities.html
Great for all Algebra. Includes Games and Video examples.
http://www.mathplayground.com/howto_InequalitiesA.html
A really clear video of how to solve inequalities
Solve for x means
Get x on its own on one side of
the inequality
So x<2 is solved.
But x+3<2 is not yet solved.
Is 3x>12 solved yet?