2010 Paper 1 Q3 - Inequalities

OK…let’s do Q3 and call it a day in terms of A maths blogging….

3.  Using a separate diagram for each part, represent on the number line the solution set of

(i) 3(2 – x) < x + 18,

(ii)  3(x² – 5) > x – 1

State the set of values of x which satisfy both these inequalities

For each of these, we need to simplify each of the inequalities. Let’s do the first one first:

(i)            3(2 – x) < x + 18

                6 – 3x < x + 18

                -3x – x < 18 – 6

                -4x < 12

                4x > -12

                x > -3

Hence, the number line looks like this:

(ii)  for the second inequality, we must remember that this is a quadratic inequality. So we must be careful with the signs.

3(x² – 5) > x – 1

3x² – 15 > x – 1

3x² – x – 14 > 0

(3x – 7)(x + 2) > 0

Hence the number line is:

 Which becomes

Hence, for the set of values of x which satisfies both inequalities, we simply look for the values of x which has an overlap. In this case, when x > 3, both inequalities are satisfied.

Hence, the solution set is {x : x Є R,  x > 3 }

Do remember that you have to put it in set notation, as they asked for the solution set. If not, you would lose marks. And since this is a one mark question, you might even lose half. Or worse, all of it!

See you tomorrow when we talk about another 3 questions….