## Slides in this set

### Slide 2

Linear inequalities:
Linear inequalities can be solved using the same algebraic methods
used to solve linear equations.
Example 1: Solve 3x + 4 < 10
Subtract 4 from both sides: 3x < 10 ­ 4
3x < 6
Divide by 3: x<2…read more

### Slide 3

Care must be taken if an inequality is multiplied or divided by a
negative quantity:
Example 2: Solve 7 ­ 2x > 3
We can subtract 7 from both sides: ­ 2x > 3 ­ 7
­ 2x > ­ 4
Divide by ­2: x < ­4 Note, the inequality
­2 must be reversed.
x<2
A better technique is to avoid the division by the negative:
7 ­ 2x > 3
Add 2x to both sides: 7 > 3 + 2x
Subtract 3 from both sides: 4 > 2x
Divide by 2: 2>x i.e. x < 2…read more

### Slide 4

The best way to solve a quadratic inequality is to use a sketch:
Example 1: Solve x2 + 3x ­ 10 < 0
Factorise to find the roots: ( x + 5 )( x ­ 2 ) < 0
So the roots are at x = ­5 or 2
Now we want the values of x where ­5 2
the quadratic is less than zero.
i.e. below the x-axis.
So x must lie between ­ 5 and 2 i.e. ­ 5 < x < 2…read more

### Slide 5

Example 2: Solve 6x ­ x2 < 8
Re-arrange: 0 < x2 ­ 6x + 8
or: x 2 ­ 6x + 8 > 0
Factorise to find the roots: ( x ­ 4 )(x ­ 2 ) > 0
So the roots are at x = 2 or 4
Now we want the values of x where
the quadratic is more than zero.
2 4
i.e. above the x-axis.
Note, that this is two separate ranges: i.e. x < 2 or x > 4…read more

### Slide 6

Summary of key points:
Linear inequalities can be solved using the same algebraic methods
used to solve linear equations.
Care must be taken if an inequality is multiplied or divided by a
negative quantity:
If it is necessary to do this, the inequality must be reversed.
The best way to solve a quadratic inequality is to use a sketch:
This PowerPoint produced by R.Collins ; Updated Apr. 2009…read more

## Similar Further Maths resources:

See all Further Maths resources »

## Slides in this set

### Slide 2

Linear inequalities:
Linear inequalities can be solved using the same algebraic methods
used to solve linear equations.
Example 1: Solve 3x + 4 < 10
Subtract 4 from both sides: 3x < 10 ­ 4
3x < 6
Divide by 3: x<2…read more

### Slide 3

Care must be taken if an inequality is multiplied or divided by a
negative quantity:
Example 2: Solve 7 ­ 2x > 3
We can subtract 7 from both sides: ­ 2x > 3 ­ 7
­ 2x > ­ 4
Divide by ­2: x < ­4 Note, the inequality
­2 must be reversed.
x<2
A better technique is to avoid the division by the negative:
7 ­ 2x > 3
Add 2x to both sides: 7 > 3 + 2x
Subtract 3 from both sides: 4 > 2x
Divide by 2: 2>x i.e. x < 2…read more

### Slide 4

The best way to solve a quadratic inequality is to use a sketch:
Example 1: Solve x2 + 3x ­ 10 < 0
Factorise to find the roots: ( x + 5 )( x ­ 2 ) < 0
So the roots are at x = ­5 or 2
Now we want the values of x where ­5 2
the quadratic is less than zero.
i.e. below the x-axis.
So x must lie between ­ 5 and 2 i.e. ­ 5 < x < 2…read more

### Slide 5

Example 2: Solve 6x ­ x2 < 8
Re-arrange: 0 < x2 ­ 6x + 8
or: x 2 ­ 6x + 8 > 0
Factorise to find the roots: ( x ­ 4 )(x ­ 2 ) > 0
So the roots are at x = 2 or 4
Now we want the values of x where
the quadratic is more than zero.
2 4
i.e. above the x-axis.
Note, that this is two separate ranges: i.e. x < 2 or x > 4…read more

### Slide 6

Summary of key points:
Linear inequalities can be solved using the same algebraic methods
used to solve linear equations.
Care must be taken if an inequality is multiplied or divided by a
negative quantity:
If it is necessary to do this, the inequality must be reversed.
The best way to solve a quadratic inequality is to use a sketch:
This PowerPoint produced by R.Collins ; Updated Apr. 2009…read more