Solve: (3x + 4√5) = 2

(3x - 4√3)

Lesson ObjectiveUnderstand about errors in roundingBe able to solve linear inequalitiesFocus in particular with issues surrounding multiplying by a variable

The formula for the time it takes for a pendulum, of length, L, to complete one oscillation,is given by the formula:

Where g is the gravitational constant on earth 9.8 ms-2 to 2 sig figs.

Suppose I measure L to be 22 cm to 2 sig figs,

What is the longest and shortest times for the pendulum to complete a single swing?

We get errors when we calculate:

Absolute error in a calculation = value obtained – true value

Relative error in a calculation =

Percentage error = × 100

More importantly we see inequality signs a lot when describing situations and we need to be able to deal with the algebra associated with them

Solve these inequalities:

1) 3x + 1 < 2x – 5

2) 7 – 2x > 4 – x

3) ½x – 3½ ≥ ¼x

4) -x – 3 < -2x – 7

Solve these inequalities:

1) 3x + 1 < 2x – 5

2) 7 – 2x > 4 – x

3) ½x – 3½ ≥ ¼x

4) -x – 3 < -2x – 7

x < 6

3 > x

x ≥ 14

x < -4

x < 0 or x > 0.5

x>-0.5 or x <-1

Important points when manipulating inequalities:

1) Never multiply both sides by a variable that might be negative!

Important points when manipulating inequalities:

1) Never multiply both sides by a variable that might be negative!

2) NEVER multiply both sides by a variable that might be negative!

Important points when manipulating inequalities:

1) Never multiply both sides by a variable that might be negative!

2) NEVER multiply both sides by a variable that might be negative!

Important points when manipulating inequalities:

1) Never multiply both sides by a variable that might be negative!

2) NEVER multiply both sides by a variable that might be negative!

3)

NEVER MULTIPLY BOTH SIDES BY A VARIABLE THAT

MIGHT BE NEGATIVE!

Important points when manipulating inequalities:

1) Never multiply both sides by a variable that might be negative!

2) NEVER multiply both sides by a variable that might be negative!

3) NEVER MULTIPLY BOTH SIDES BY A VARIABLE THAT

MIGHT BE NEGATIVE!This does beg the question, how then do we

deal with things like:

where the variable is ‘underneath’?

2𝑥 <4

So what should you do?

Method 1:Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide what range of values satisfy the inequality.

Eg 1 Draw the curves y = and y = 4

So what should you do?

Method 1:Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide what range of values satisfy the inequality.

Eg 2 Draw the curves y = and y = 3

Solve these inequalities:

1) 2x – 3 > 3x

2) 1 - x < x + 7

3)

Solve these inequalities:

1) 2x – 3 > 3x

2) 1 - x < x + 7

3)

x < -1

-3 < x

x< 0 or x > 1/3

x <-1 or x > -2/3

0 < x < 0.4

x 2.5 or x < 2

-3 < x - 2.5

So what should you do?

Method 1:Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide for what range of values the inequality is satisfied.

OR

Method 2:Multiply both sides by the square of the variable because we know that the square will be positive, no matter if the original was negative

Fine for single maths

Eg 1

So what should you do?

Method 1:Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide for what range of values the inequality is satisfied.

OR

Method 2:Multiply both sides by the square of the variable because we know that the square will be positive, no matter if the original was negative

OR

Method 3:Collect everything as a single term on one side of the inequality by adding, subtracting and factorising. Then use a table to determine when the inequality is satisfied.

Advanced Technique

Fine for single maths

Lesson ObjectiveBe able to solve quadratic inequalities

Eg 1 Solve 2x2 < 5x + 12

Hence solve a) 2x2 – 5x – 12 ≤ 0

b) 2x2 – 5x – 12 > 0

Lesson ObjectiveBe able to solve quadratic inequalities

Eg 1 Solve 2x2 < 5x + 12

Hence solve a) 2x2 ≤ 5x + 12

b) 2x2 > 5x + 12

Draw/sketch a graph, then think of solving the inequality as an equation and use the graph to decide for what range of values the inequality is satisfied.

Solve these inequalities:

1) x2 < 16

2) x2 ≥ 25

3) x2 + 4x > 0

4) x2 – 3x ≤ 0

5) x2 – 5x + 4 < 0

6)

7) 3x2 < 2 – 5x

8) 4x – 3 ≥ x2

9)

10)

Solve these inequalities:

1) x2 < 25

2) x2 ≥ 7

3) 2x2 < 9x + 5

4) 6x2 – x – 1 > 0