Solve the inequality - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Next, we find the roots of the equation by setting the factors equal to zero:

$x - 6 = 0\Rightarrow x = 6$
$x + 1 = 0\Rightarrow x = -1$

These roots divide the number line into three intervals:

1. $(-\infty, -1)$
2. $(-1, 6)$
3. $(6, \infty)$

We will test each interval to determine where the product $(x - 6)(x + 1)$ is less than zero.

• For the interval $(-\infty, -1)$, let’s test $x = -2$:
  • $(-2 - 6)(-2 + 1) = (-8)(-1) > 0$
• For the interval $(-1, 6)$, let’s test $x = 0$:
  • $(0 - 6)(0 + 1) = (-6)(1) < 0$
• For the interval $(6, \infty)$, let’s test $x = 7$:
  • $(7 - 6)(7 + 1) = (1)(8) > 0$

Therefore, the inequality holds in the interval $(-1, 6)$.

The solution to the inequality is:

$-1 < x < 6$