By Jan Gerards | Updated Aug 30, 2022
In algebra, “annex” refers to appending a number to both sides of an equation. Depending on the context, this can mean adding or multiplying by the same value, thereby preserving equality.
Starting with the equation 2x + 6 = 4y + 16, you can annex a number to both sides by adding it. For instance, adding 4 to each side yields:
2x + 10 = 4y + 20
This simple operation keeps the equation balanced and can help isolate variables later.
When a calculation involves multiplication, annexing can involve multiplying each side by a common factor. Consider the identity 44,670 × 5 = 223,350. By annexing a zero—multiplying both sides by 10—you get:
446,700 × 5 = 2,233,500
Dividing the result by 2 restores the original product, illustrating how annexation can simplify work with large numbers.
Adding the same value to both sides allows you to transform the equation into a form that is easier to solve. For example, from 2x + 10 = 4y + 20 we can rearrange to:
2x – 4y = 10
Now the equation is ready for standard algebraic techniques such as factoring or substitution.
Annexing through multiplication is especially handy when a multiplication factor is cumbersome. Using the earlier example, computing 44,670 × 5 can be done by:
(44,670 × 10) ÷ 2 = 446,700 ÷ 2 = 223,350
This strategy turns a difficult multiplication into a simpler division, leveraging the fact that multiplying by 10 is trivial and dividing by 2 is often quicker.
