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Year 7 Interactive Maths - Second Edition


Equations Involving Division

Consider the equation
30 - 20 = 10

Clearly both the left-hand side and right-hand side equal 10.  That is LHS = RHS

If we double the weight on both sides, then we obtain:
2(30 - 20) = 2 × 10

The left-hand side and the right-hand side both equal 20.  Therefore, LHS = RHS

We notice that the statement
30 - 20 = 10
remains a true statement when each side of the equation is multiplied by 2.

This suggests that equations behave like balances.  If the same number multiplies the mass in both scales of a balance, it still remains balanced.  This implies that we can multiply both sides of an equation by the same number to get a new equation.


Consider the equation x/2 = 9.
If you put x/2 kg in one of a pair of scales and add 9 kg to the other, the scales will show that x/2 kg is equal to 9 kg.  That is x/2 = 9

Doubling the weight in both scales of the balance will result in x kg on one scale and 18 kg on the other.  The scales will show that x kg = 18 kg.  That is x = 18

After doubling the weight in both scales, the scales remain balanced.


From the preceding discussion, we can state that:

To solve an equation, we can multiply both sides of an equation by the same number.


Example 6

Solve the equation x/9 = 8 for x.

Solution:

Multiply both sides by 9 to find x = 72.


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