solve: (3x + 4√5) = 2 (3x - 4√3). lesson objective understand about errors in rounding be able...
DESCRIPTION
Lesson Objective Understand about errors in rounding Be able to solve linear inequalities Focus in particular with issues surrounding multiplying by a variableTRANSCRIPT
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