1. (a) Solve 14n > 11n + 6 (b) On the number line below, show the set of values of x for which -2 < x + 3 ≤ 4. - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 2

First, we simplify the compound inequality:

1. For the left part, we solve -2 < x + 3:

   • Subtract 3 from both sides: $-2 - 3 < x$ $-5 < x$ This means x must be greater than -5.

2. For the right part, we solve x + 3 ≤ 4:

   • Subtract 3 from both sides: $x ≤ 4 - 3$ $x ≤ 1$

Combining both parts, we have: $-5 < x ≤ 1$

On the number line, represent this as an open circle at -5, showing that it is not included, and a closed circle at 1, indicating that 1 is included, with a line segment connecting the two to represent all values of x in that range.