Inequations

When solving inequations, the inequality sign can mostly be treated the same way as an equals sign.

Solve the inequation \(3x + 2 \le - 4\)

\(3x + 2 \le - 4\)

\(3x \le - 4 - 2\)

\(3x \le - 6\)

\(x \le \frac{{ - 6}}{3}\)

\(x \le - 2\)

Solve the inequation \(2x-1\,\textgreater 9\)

\(2x\,\textgreater 9+1\)

\(2x\,\textgreater 10\)

\(x\,\textgreater \frac{10}{2}\)

\(x\,\textgreater 5\)

As stated previously, the same rules for equations can be applied to inequations apart from one exception:

When multiplying (or dividing) an inequation by a negative number, switch the inequality symbol round.

For example, greater than (>) becomes less than (<).

Now try the example question below.

Question

Solve the inequation \(5(w - 1) - 8w \ge - 11\)