What is the inequality for "q is less than or equal to -1"?

The inequality for "q is less than or equal to -1" is written as \( q \leq -1 \).

In mathematics, inequalities are used to show the relationship between two values when they are not equal. The symbol \( \leq \) means "less than or equal to." So, when we say \( q \leq -1 \), we are indicating that the value of \( q \) can be any number that is either less than -1 or exactly equal to -1.

To visualise this on a number line, you would draw a line and mark the point at -1. You would then shade the line to the left of -1 to show all the numbers that are less than -1. Additionally, you would place a closed circle (or dot) on -1 to indicate that -1 is included in the set of possible values for \( q \).

In practical terms, if you were solving an equation or a problem and you ended up with \( q \leq -1 \), you would know that any number like -2, -3, -4, and so on, as well as -1 itself, would satisfy the inequality. This is useful in various mathematical contexts, such as solving equations, graphing functions, and analysing data sets.

Understanding inequalities is a fundamental skill in GCSE Maths, as it helps you to describe and work with ranges of values rather than just specific numbers. This can be particularly useful in real-world scenarios, such as determining acceptable ranges for measurements or analysing trends in data.