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Year 7 Interactive Maths - Second Edition


Equations Involving Subtraction

Consider the equation
20 - 4 = 2 × 8

Clearly both the left-hand side and right-hand side equal 16.  That is LHS = RHS

If we add 4 to both sides of the equation, then we obtain:
20 - 4 + 4 = 2 × 8 + 4

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

We notice that the statement
20 - 4 = 2 × 8
remains a true statement when 4 is added to both sides of the equation.

This suggests that equations behave like balances.  If the same mass is added to each scale of a balance, it still remains balanced.  This implies that we can add the same number to both sides of an equation to get a new equation.


Consider the equation x - 6 = 9.

If you put (x - 6) kg in one of a pair of scales and add 9 kg to the other, the scales will show that (x - 6) kg is equal to 9 kg.  That is x - 6 = 9

Adding 6 kg to each scale will result in x kg on one scale and 15 kg on the other.  The scales will show that x kg = 15 kg.  That is x = 15

After adding 6 kg to both scales, the scales remain balanced.


From the preceding discussion, we can state that:

The same number can be added to both sides of an equation.


Example 4

Solve the equation x - 8 = 15 for x.

Solution:

Add 8 to both sides to find x = 23

 

Study Another Topic in Chapter 7: Equations

Equations ] Solution of Equations ] [ Equations Involving Subtraction ] Equations Involving Multiplication ] Equations Involving Division ] Solving Word Problems ] Problem Solving Unit ] Symbols ] Index ]

 

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