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© Boardworks 2012
Solving linear equations
Linear equations are the easiest type of equation to solve
because the unknown is not raised to any power other than 1.
We can solve very simple linear equations by inspection.
For example:
19 – x = 8
x = 11
7x = 42
x=6
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We think of this as: “What
number subtracted from 19
gives us an answer of 8?”
We think of this as:
“What number
multiplied by 7 gives
us an answer of 42?”
© Boardworks 2012
Using inverse operations
For more tricky equations, use inverse operations to solve
the equation in several steps.
Perform the same operations on both sides of the equals sign
to keep the equation balanced. Aim to get the unknown on one
side and a number on the other.
For example:
subtract 5 from both sides:
4x + 5 = 29
–5
–5
4x = 24
divide both sides by 4:
÷4
÷4
x=6
Check that 4 × 6 + 5 is equal to 29 in the original
equation to verify your answer.
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Balance the scale
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Careful, don’t slip up!
Look at this equation:
divide both sides by (x – 1):
(x – 1) = 2(x – 1)
1=2
This is false. What has gone wrong?
Explain your answer.
Notice that the solution to this
equation is x = 1, so when we divided
by (x – 1), we in fact divided by zero.
This is not allowed.
Next time someone “proves” to you
that 1 = 0, watch out! They probably
divided by zero.
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Equation solving
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Weekly allowance
Anna gets a $7 weekly allowance
and already has $48.
She spends $2 a week on sweets.
Her brother Charlie also gets
$7 a week. He has no money
saved at the moment, but
spends nothing each week
from now on.
In how many weeks will Anna and Charlie both have the
same amount of money?
How much will they each have at this point?
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Equivalent expressions
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Comparing ages
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