Algebra - SolvingNotes and catch up work – if you were on ODE you need to read this!

What is an equation?Why is this an equation that can be solved;

but this is not;

???Because…an equation must have an equals sign in it.

1. Linear EquationsAn equation is linear if the highest power of is just plain “” or “”.

To solve a linear equation just remember the golden rule: whatever you do to one side or an equation, you must do exactly the same to the other.Basically – keep the equation balanced!

1. Linear EquationsTechnique:

Get x’s on one side of the equation and numbers on the other.

You may first need to do things like expanding brackets, adding like terms or removing fractions.

1. Linear EquationsExampleSolve:

expand the brackets and add like terms

move numbers to right by adding 6 to both sides move x’s to

left by adding 2x to both sides

to get x on it’s own divide both sides by 9

1. Linear Equations – with Fractions! We need to be careful when working with

equations involving fractions.

Before solving you need to remove the fractions.1. Find the lowest common denominator (CD)2. Multiply everything in the equation by the CD3. Do any cancelling4. You should now have a nice easy linear

equation to solve.

1. Linear Equations – with Fractions!

ExampleSolve

Now just solve as normal. Answer:

CD = 20

x 20 x 20 x 20

x 20

x 205 x 204 x 20 10

x 20

Multiply every term by CDDo any cancellation

1. Linear EquationsPractice Work:Homework book p 81 and 82Also try solving the following:

2. Linear InequationsAn inequation (or inequality) is very similar to an equation, except for the presence of one of the following signs: > means greater than means greater than or equal to < means less than means less than or equal to

2. Linear InequationsUse the same general technique

Get x’s on one side, numbers on the other Whatever you do to one side, do the same

to the other

BUTIf you divide or multiply by a negative number the inequality sign must change direction.

2. Linear InequationExampleSolve

-5

move numbers to right by adding 4 to both sides

move x’s to left by subtracting 5x from both sidesto get x on it’s

own divide both sides by -2

You divided by -2 so sign needs to swap direction

2. Linear InequationsPractice work:Homework book p83Also try solving the following:

3. Quadratic Equations (that can be factorised)This is revision of Y11 material.Recall: A quadratic equation has as the highest power.Examples of quadratics:

Recall: A quadratic equation should have two solutions (sometimes called roots)

3. Quadratic Equations (that can be factorised) Technique for solving:1. Rearrange the equation so it is equal to

zero (i.e. get everything on one side.)2. Factorise 3. Put each bracket equal to zero

To check your answers sub each one (separately) into the equation.

3. Quadratic Equations (that can be factorised)ExampleSolve

or

move everything to left by subtracting 18 from both sides

factorise

put each bracket =0 and solve

3. Quadratic Equations (that can be factorised)Practice WorkHomework book p97Also try solving the following:

4. Quadratic Equations – with quadratic formula

If you cannot find easy factors for a quadratic then don’t worry – they might not exist!

You can always use the quadratic formula instead:

4. Quadratic Equations – with quadratic formula

Given the quadratic equation

we can get the two solutions using this formula: