<h3>Inequalities</h3><p>An <strong>inequality</strong> uses <code><</code>, <code>></code>, <code>≤</code> or <code>≥</code>. Solve <code>2x - 1 < 7</code> by adding 1 then dividing by 2 to get <code>x < 4</code>. <strong>Golden rule:</strong> if you multiply or divide both sides by a negative number, reverse the inequality sign.</p><h3>Simultaneous equations</h3><p>Two <strong>simultaneous equations</strong> share one solution. By <strong>elimination</strong>, solve <code>x + y = 10</code> and <code>x - y = 4</code>: add them to get <code>2x = 14</code>, so <code>x = 7</code> and <code>y = 3</code>. By <strong>substitution</strong>, make x the subject of one equation and put it into the other.</p><div class="callout"><strong>Kenyan context:</strong> A trader sells mangoes at KSh 20 and oranges at KSh 15. If she sells x mangoes and y oranges, and <code>x + y = 100</code> fruits for total sales of <code>20x + 15y = 1700</code>, solving simultaneously gives x = 40 mangoes and y = 60 oranges. An inequality also helps budgeting: if a student has KSh 200 and a textbook costs KSh 30 each, then <code>30n ≤ 200</code> means she can buy at most 6 books.</div>