year 8 maths

2E
Equations with brackets
83
2E Equations with brackets
In Chapter 1 it was noted that expressions with brackets could be expanded by considering
rectangle areas.
The diagram shows that 4(x + 2) and 4x + 8 are equivalent. This becomes quite helpful when solving an
equation like 4(x + 2) = 5x + 1 . We just solve 4x + 8 = 5x + 1 using the techniques from the previous
section.
x 2
4
4 × x = 4x
4 × 2
= 8
Area = 4(x + 2)
Area = 4x + 8
Let’s start: Architect’s dilemma
In the house plans shown, the kitchen and dining room are separated by a dividing door.
7 Dining room
4
3
Kitchen
4
Divider
• If the breadth of the divider is x , what is the area of the kitchen? What is the area of the dining room?
• Try to find the breadth of the divider if the areas of the two rooms are equal.
• Is it easier to solve 3(7 + x) = 4(x + 4) or 21 + 3x = 4x + 16 ? Which of these did you solve
when trying to find the breadth of the divider?
■ To expand brackets, use the distributive law , which states that:
• a(b + c) = ab + ac
For example, 3(x + 4) = 3x + 12 .
• a(b − c) = ab − ac
For example, 4(b − 2) = 4b − 8 .
Key ideas
■ Like terms are terms that contain exactly the same pronumerals and can be collected to
simplify expressions. For example, 5x + 10 + 7x can be simplified to 12x + 10 .
■ Equations involving brackets can be solved by first expanding brackets and collecting
like terms.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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