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Year 9 Mathematics
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Equations
Learning Intentions
• Pupils should be able to:
 Simplify algebraic expressions by collecting like terms and removing
brackets
 Interpret and apply simple rules expressed in words to generate a
numerical solution
 Generate and use a simple formula to find connections between two
or more variables
 Formulate and solve linear equations originally expressed in words
 Solve equations involving brackets, terms on both sides, re-ordering
and collecting like terms
 Solve linear inequalities representing solution on number line
Collecting Like Terms
• A Mathematical expression uses numbers and
letters to represent numbers
• Expressions are used to solve problems
• Example:
• We represent the following as 4a + 3c. (4 apples and 3
cars
More Terms
• Sometime we need to combine all the terms
together
• Simplify the following:
• 3c + 2a + 4c + 3a
Simplify
• 4a + 5a – 2a
• 10x – 2x + 3x
• 5a + 4x – 2a + 5x
• 7a – 3x + 2x – 8a
• 9x2 – 3x + 5x + 2x2
• -3x2 + 5x – 5x2 + 10x2
Brackets!
• Sometimes we use brackets
• Simplify the following:
• 2(3a + 2p) =
Simplify
• 4(3x + 4b)
• 5(x + 4)
• 3(2x – 5)
• 2x + 3(x + 2)
• 5(2x + 4) – 8x
• 12x – 2(x + 3)
• 18x – 3(5 + x)
• 20x – 4(3 – x)
Solving Equations
• An equation means that two things are equal.
• A pair of scales is sometimes used to show
equations because when both sides balance they
are equal.
• If you put something else on one side, you must
put the same amount on the other side or the
scales are no longer balanced.
• If you take something off one side, you must take
the same amount off the other side or the scales
are no longer balanced.
Solving Equations
• Look at the scales
• We can write:
• 2x + 2 = 6
• If you take two marbles
off each side you get
• 2x = 4
• If you now take each side
and divide by two you get
• x=2
x x
Show your working out
• Lets look at that equation again
2x + 2 = 6
( – 2)
2x = 4
( ÷ 2)
x=2
Another example
• Solve: 2 = 3x – 16
What about negatives!
• Solve: 3x + 15 = 3
Who has the most?
• Solve: 6x + 26 = 4x
Try that again
• Solve: 4 = 16 – 3x
What about fractions?
• Solve: 7x + 20 = 26
And brackets!
• Solve: 3(2x + 1) = 15
Some more!
• Solve 3(4 – 3x) = 3
More terms
• Solve: 4x + 3 = 2x + 11
More brackets
• Solve: 8(x + 1) = 2 (x – 16)
Help!
• Remember when solving equations
• DO THE SAME TO BOTH SIDES
• Expand brackets and Simplify
• Deal with LETTERS first (keep on side where are most)
• Deal with NUMBERS after (remove numbers on same
side as letters)
• get ‘single letter = ’ (leave as fraction if you need to)
Problems
• Sometimes we are given practical examples.
• We need to create the equation and then solve it.
• Example:
• A bus costs £200 to hire for the day. A hockey club
charges £10 for each non member (n) and £6 for
each member (m) to go on an outing.
a. Write down an equation for the cost of hiring the bus
b. If 20 members go on the outing, how many nonmembers need to go if the club is not to lose money?
Where did the equals go?
• Sometimes the answer to a problem has a number
of solutions.
• If the cost of a cinema ticket is £6, then you must
have £6 or more to go (everyone wants popcorn
and coke!)
• We can write this as:
• Money ≥ 6
Using the number line
• We often illustrate this answer using a number line
Too big
• Sometimes vehicles must be less than a certain
height to let them into a car park.
• The height of the vehicle may need to be less than
2 m.
• We can write this as
• height < 2 m
• And show it on the number line:
• Remember: more ink – solid, less ink - hollow
Both Sides
• Sometimes two inequalities are combined into one.
• For example:
• x>2
• x≤8
• Are often combined to:
• 2<x≤8
• We represent this on the number line as:
Solving Inequalities
• Sometimes we need to simplify inequalities.
• We do this the same way as equations – it’s just the
sign is different!
• Example:
• x–5<3
• x – 5 < 3 (+5)
• x<8