Review question

# Can we solve $12/(x-3) < x+1$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7035

## Suggestion

1. Find the solution set for $x$ given that the following three relations for $x$, $y$, where $x, y \in \mathbb{R}$, are simultaneously true: $\begin{equation*} y < x + 1, \quad y + 6x < 20, \quad x = 5y - 7. \end{equation*}$

We might get some useful insight into what is happening here by drawing a sketch.

1. Find the solution set of the inequality $\begin{equation*} \frac{12}{x-3} < x + 1, \quad (x \in \mathbb{R}, x \ne 3). \end{equation*}$

Again, a sketch might be helpful here, to help check that our answer is sensible. Remember that $x-3$ might be positive or negative.