Notesale: Turn your study into money

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How to solve linear equations
Properties of equalities
Two equations that have the same solution are called equivalent equations e
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5 +3
= 2 + 6
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An inverse operation are two operations that undo each other e
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addition and
subtraction or multiplication and division
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5+3−2=6+2−2
This gives us a couple of properties that hold true for all equations
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𝑖𝑓 𝑎 + 𝑏 = 𝑐 𝑡ℎ𝑒𝑛 𝑎 + 𝑏 − 𝑏 = 𝑐 − 𝑏, 𝑜𝑟 𝑎 = 𝑐 − 𝑏

As well as it goes for the multiplication property of equality
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𝑖𝑓

𝑎
𝑎
= 𝑐, 𝑎𝑛𝑑 𝑏 ≠ 0, 𝑡ℎ𝑒𝑛
𝑏 = 𝑐 x 𝑏, 𝑜𝑟 𝑎 = 𝑐𝑏
𝑏
𝑏

And naturally this goes for the division property of equality as well
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Anything is acceptable
as long as you do the same thing on both sides
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He now wants to chop it into smaller
pieces
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And then he continues on
into making ten pieces that all are 6ft long before loading them onto his truck
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60=30+30=6+6+6+6+6+6+6+6+6+6
This is called the reflexive property of equality and tells us that any quantity is equal to
itself
𝑎=𝑎
We can also use this example with the pieces of wood to explain the symmetric property
of equality
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𝑖𝑓 𝑎 = 𝑏, 𝑡ℎ𝑒𝑛 𝑏 = 𝑎
Or if we use our example
𝑖𝑓 60 = 30 + 30, 𝑡ℎ𝑒𝑛 30 + 30 = 60
Another property that can be explained by this is the transitive property of equality
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𝑖𝑓 𝑎 = 𝑏 𝑎𝑛𝑑 𝑏 = 𝑐, 𝑡ℎ𝑒𝑛 𝑎 = 𝑐
Or in the numbers taken from the oak tree example

𝑖𝑓 60 = 30 + 30
𝑎𝑛𝑑 30 + 30 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6
𝑡ℎ𝑒𝑛 60 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6
Since we know that 30 + 30 = 20 + 40 and that 30 + 30 = 60 we can substitute 30 + 30
for 20 + 40 and get 60 = 20 + 40
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If a = b, then a can be substituted for b in any expression
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Thus we use the common symbols for velocity (v), distance (d)
and time (t) and express it thus:

𝑣=

𝑑
𝑡

We may simply describe a formula as being a variable and an expression separated by
an equal sign between them
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Example
A book club requires a membership fee of $10 in addition to the $2 levied for each
book ordered

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