1. Solve the equation ax + b = c to find x in terms of a, b and c.
Equations
A2.2 Extension Plenary
ax + b = c (where a, b and c are numbers) is a formula for simple equations.
For 3x + 4 = 16 a = 3, b = 4 and c = 16.
Solve the equation ax + b = c to find x in terms of a, b and c.
(You will end up with a formula for solving equations.)
Use your formula to find the solution to 6x + 4 = 28.
Check that your solution is correct by using your usual method to solve the equation.
Try your formula on these two equations. 2x + 5 = 12
6x + 15 = 36
What do you notice?
Preamble
An activity to encourage pupils’ algebraic thinking. Some pupils may require support while, as an extension of the task, the most able can be challenged to find the “formula” to solve the general linear equation ax + b = cx + d. The activity gives the opportunity to use correct mathematical vocabulary.
Possible content
Elementary algebraic manipulation and the solution of simple linear equations.
Resources
None.
Solutions/Notes
The solution to 6x + 4 = 28 is x = 6.
The two equations have the same solution, x = 3½.
The extension equation ax + b = cx + d has solution