Why do this problem?

Although inequalities look visually like equations, inequalities do not work in the same way that equations do. This question will lead students to realise that inequalities must be manipulated in different ways.

Possible approach

You might suggest trial and error to get started, or begin with one of the key questions.

You can also let the students try 'algebraic' approaches in which the equation is rearranged to given


x2 -2x-3<0

This would lead to
(x-3)(x+1)<0

which would appear to imply that

-1<x<3

Students would then need to work out why this is in conflict with the fact that direct substitution of -0.5 clearly does not provide a valid answer.

You might also encourage a numerical experiement, which should be backed up by a proper analysis.

Key questions

How does this question relate to quadratic equations?

Can we find some values which work and some values which do not work?

Possible extension

Can you extend this to find the 'solution' to the general inequality ax+ b x <c

Possible support

Tabulate the values between -10 and 10 to see which of these integers satisfy the inequalities

The lesson could be steered to focus on one of more of these processes

Students may try
work logically towards results and solutions, recognising the impact of constraints and assumptions manipulate numbers, algebraic expressions and equations and apply routine algorithms identify the mathematical aspects of the situation or problem
Students must always remember that all inequalities must be satisfied. There are several if-then cases to consider Students will need to focus on how to multiply each side of an inequality by a positive or negative number Students will need to appreciate that inequalities work in different way to equations when negative numbers are involved