April 10, 2023

Equations with brackets

1. Equations with brackets.

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April 10, 2023

This is an equation. It is a statement that two numbers, or expressions, in this case about biscuits, are equal.

= +

Here are two lots of biscuits

The group of 3 on the left is the same as the 1 plus the other 2 on the right.

What is on one side of the equals sign is the same as what is on the other side.Notice how the word equation and the word equal are very similar.

Revise

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April 10, 2023

Here is another equation.

=

Imagine we represented each snickers with the letter “s”.

=s s s++

3You can work out what 1 snickers bar would cost by dividing both sides of the equation by 3.

s =

Revise

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April 10, 2023

When you use a letter to stand for a number, or an object, you are using algebra.

+ 20p = £24nHow would you find out what 4 packets of nuts come to?

You can take 20 pence from the left hand side, but you also need to take 20 pence from the right hand to keep both sides equal.

£1.80

And if four packs of nuts are £1.80, then one pack of nuts is £1.80 ÷ 4.

n 45p

Revise

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April 10, 2023

Solve this simple equation 3x + 4 = 16

Take 4 from both sides.

Divide both sides by 3.

To solve an equation you need to simplify it until there is a letter on one side of the equals sign and a number on the other.You do this by performing successive, operations to each side of the equals sign.

3x = 12

x = 4

You have used the opposite operation of “+ 4” and then the opposite operation of “× 3”.

Revise

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April 10, 2023

A quicker method is to start by dividing both sides by the number outside the brackets.

( ) = 12x + 23Sometimes you need to solve an equation that has brackets in it. ( )3 x + 2 = 12

First you need to expand the brackets.This means multiply everything inside the brackets by the number on the outside.

3x + 6

Subtract 6 from both sides. 3x

Divide both sides by 3

= 6

x = 2

( ) =x + 23

Expanding the brackets first is the most reliable and accurate way to solve an equation like this.

124x 2

Explanation

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April 10, 2023

xYou may need to solve an equation that has the unknown on both sides. ( ) =3 x+ 2 + 5Start by expanding the brackets.

3x = x -1

2x = -1

x = -0.5

x( ) =3 x+ 2 + 53 6

You can then work through the equation this way.

Subtract 6 from both sides.

Subtract x from both sidesDivide both sides by 2.

After expanding the brackets, you could also proceed through this equation by subtracting 5 from both sides, or subtracting x from both sides.

When the unknown is on both sides.Explanation

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