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Year 10 Interactive Maths - Second Edition


Equations Involving Two or More Operations

To solve a linear equation, we apply the same operations to both sides of the equation to collect numerical terms on the right-hand side and pronumeral terms on the left-hand side.

Example 5

Solve 2p + 7 = 20 for p.

Solution:

Subtract 7 from both sides and then divide both sides by 2 to find p = 6 1/2.

Setting Out:

We can set out the solution as follows:

The solution can be set out in three lines.

Check:

LHS = 2p + 7 = 2 times 6.5 + 7 = 20 = RHS, so our solution, p = 6 1/2, is correct.


Example 6

Solve 8x + 3 = 5x + 18 for x.

Solution:

Subtract 3 from both sides, then subtract 5x from both sides and finally divide both sides by 3 to find x = 5.

Setting Out:

We can set out the solution as follows:

The solution can be set out in four lines.

Check:

Substitute x = 5 into the LHS to find LHS = 43.

Substitute x = 5 into the RHS to find RHS = 43.

Therefore, LHS = RHS.  So, our solution, x = 5, is correct.


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